Free Printable Worksheets for learning Logic at the College level

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Logic

Introduction

Logic is a branch of philosophy that deals with reasoning, argumentation, and the principles of valid inference and demonstration. It is concerned with understanding the nature of reasoning and the ways in which arguments can be constructed, evaluated, and justified.

Key Concepts

Argument: A set of claims that are presented in order to establish a conclusion.
Premise: A claim or statement that is offered in support of a conclusion.
Conclusion: The claim that is being supported by the premises in an argument.
Valid Argument: An argument in which the conclusion necessarily follows from the premises.
Sound Argument: A valid argument with true premises.

Types of Arguments

Deductive: An argument in which the conclusion is necessarily true if the premises are true.
Inductive: An argument in which the conclusion is supported by the premises, but is not necessarily true if the premises are true.
Abductive: An argument in which the conclusion is the best explanation for the given evidence.

Common Logical Fallacies

Strawman Fallacy: Misrepresenting or distorting an opponent's argument in order to make it easier to refute.
Ad Hominem Fallacy: Attacking the person rather than their argument.
Appeal to Authority Fallacy: Using the opinion of an authority figure as evidence without providing additional supporting evidence.
False Dichotomy Fallacy: Presenting only two options when others exist.

Tips for Constructing Arguments

Clearly state your premises and conclusion.
Make sure your premises are relevant and provide adequate support for your conclusion.
Consider counterarguments and address them in your argument.
Use clear and concise language.
Use valid forms of logical inference.

Conclusion

Understanding the principles of logic is essential for clear thinking and effective communication. By familiarizing yourself with key concepts, types of arguments, common fallacies, and tips for constructing arguments, you can improve your ability to reason and make persuasive arguments.

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Word	Definition
Deduction	A logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true. For example, if all men are mortal and Socrates is a man, we can use deduction to conclude that Socrates is mortal.
Induction	The process of reasoning from a specific premise to a general conclusion. Unlike deduction, induction makes claims based on over-arching principles rather than specific instances. For example, based on the observation that all swans that we have seen are white, we might induce the conclusion that all swans are white.
Syllogism	A form of reasoning where a conclusion is drawn from two given or assumed propositions (premises). The conclusion is valid only if both premises are true. For example, All humans are mortal and Socrates is human both include the term human so we may infer the conclusion Socrates is mortal.
Fallacy	A type of mistake in reasoning that invalidates an argument or claim. Often, fallacies occur in arguments where the premises are not valid or the conclusion doesn't follow from the premises. Examples of fallacies include ad hominem attacks, appeals to emotion, and false analogies.
Proposition	A statement that is either true or false, such as The earth orbits around the sun. Propositions are used in logic to make premises that support conclusions.
Premise	A statement or proposition that is used to support a conclusion in a logical argument. For example, in the argument All men are mortal. Socrates is a man. Therefore, Socrates is mortal, the first two statements are premises that lead to the conclusion of the argument.
Conclusion	A statement that is reached through logical reasoning. For instance, given two propositions or premises, a conclusion would deduce to either of the two possibilities.
Validity	The quality of an argument where the premises logically flow to the conclusion. In a valid argument, if the premises are true, then the conclusion reached will also be true.
Soundness	Condition when an argument is valid and all its premises are true. Sound reasoning is a reliable way to come to a conclusion about a fact or topic.
Propositional Logic	Also called statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions or statements, as well as the implications of such operations. For instance, in propositional logic, a proposition would be defined as either true or false, and unlike other forms of logic, it cannot involve any internal structures.
Predicate	In logic, a predicate is a term that refers to something about a subject, which forms a statement or proposition when combined with that subject. For example, in the statement Alice drinks coffee, the predicate is drinks coffee.
Counterexample	An example that refutes or disproves a proposition or theory. For example, if someone were to say that all swans are white, a black swan would be a counterexample because it defies the claim.
Paradox	A statement or proposition that contradicts itself or defies intuition. Famous examples include the liar paradox, which states that this sentence is false, and the unexpected hanging paradox, which involves a person who knows they will be hanged on one of the weekdays of a particular week but not knowing which day.
Modus Ponens	A form of deductive reasoning where the conclusion of an argument is deduced from two premises, one of which asserts a conditional statement such as if p, then q and the second asserts that the antecedent (p) is accurate.
Modus Tollens	A form of deductive reasoning where the conclusion of an argument is deduced from two premises, one of which asserts a conditional statement such as if p, then q and the second asserts the negation of the consequent (not q).
Counterfactual	A conditional statement that usually starts with the phrase If it had been the case that ... and describes a circumstance that did not happen, often used to speculate the outcome of hypothetical situations.
Enthymeme	A form of reasoning where the conclusion is not explicitly stated but is implied by the premises; often used in persuasive discourse. For example, if someone were to say He studies hard. Therefore, he will pass the exam, the implied premise is students who study hard will pass their exams.
Reasoning	The use of critical thinking or rationality to analyze and interpret information, often with the goal of drawing conclusions or making decisions.
Antecedent	A term that refers to the component of a hypothetical conditional statement (if... then), residing on the left of the implication sign. In the statement if it's raining outside, then John carries an umbrella, the antecedent is It's raining outside.
Consequent	The component that refers to the right side of the implication sign in a hypothetical conditional statement (if... then). In the statement if it's raining outside, then John carries an umbrella, the consequent is John carries an umbrella.

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Logic Study Guide

Introduction to Logic

Logic is a branch of philosophy that deals with the study of reasoning, argumentation, and the principles of proper inference. Before diving into the various aspects of logic, it's essential to have a good rundown of what it represents, its history and why it's an important subject to study.

Key Concepts

Reasoning
Argumentation
Inference
Propositions
Premises
Conclusions
Deductive reasoning
Inductive reasoning

History of Logic

Logic as a subject of study dates back to ancient Greece, where philosophers such as Aristotle and Socrates made significant contributions to its development. Over the years, the study of logic has continued to evolve, with advancements being made in both formal and informal reasoning.

Types of Reasoning

Deductive Reasoning

Deductive reasoning is a type of reasoning that involves starting with general principles and working your way to a specific conclusion. It's sometimes referred to as top-down reasoning. The study of deductive reasoning involves learning how to construct valid arguments and identify fallacies in reasoning.

Inductive Reasoning

Unlike deductive reasoning, inductive reasoning involves starting with a specific observation or set of observations and working to identify a general principle. It's sometimes referred to as bottom-up reasoning. The study of inductive reasoning involves learning how to assess the strength of an inductive argument and identify common fallacies.

Abductive Reasoning

Abductive reasoning is a type of reasoning that involves making an inference to the best explanation. It is used to explain the observations that may not be fully explained by a given hypothesis. Its study involves learning how to determine which hypothesis is the most likely in light of the evidence presented.

Types of Argument

Deductive Argument

A deductive argument is an argument that aims to show that its conclusion must necessarily follow from its premises. For example, All men are mortal, Socrates is a man, therefore Socrates is mortal. The study of deductive argument involves learning how to identify, construct, and evaluate valid and invalid forms of deductive reasoning.

Inductive Argument

An inductive argument is an argument that aims to show its conclusion is probable or likely based on its premises. For example, 85% of students in this college voted for John, therefore John is likely to win the election. The study of inductive argument involves assessing the strength of inductive arguments and the potential for error.

Fallacies

A fallacy is an error in reasoning that leads to a false argument. The study of fallacies involves learning how to identify the various types of fallacies and how to avoid them.

Types of Fallacies

Ad Hominem
Strawman
Appeal to Authority
False Dichotomy
Slippery Slope
and more

Symbolic Logic

Symbolic logic is the traditional tool for studying logical reasoning. It involves the use of symbols, such as letters or shapes, to represent logical concepts. Its study involves learning how to translate arguments into formal symbols and assess their validity.

Propositional Logic

Propositional logic is a type of symbolic logic that deals with propositions or statements that can be either true or false. It's mainly concerned with developing rules for combining and negating propositions to form complex arguments.

Predicate Logic

Predicate logic, on the other hand deals with more complex arguments that involve relationships between objects. Its study involves learning how to express these relationships using logical notation and symbol.

Conclusion

The study of logic is fundamental to understanding how to reason effectively and evaluate persuasive arguments critically. By learning the various types of reasoning, arguments, fallacies, and symbolic logic, you will be able to develop solid critical thinking skills that will be useful across different areas of study.

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Practice Sheet for Logic

Instructions: Try to solve the following problems to practice your skills in logic.

Translate the following into symbolic logic: Either Sarah is a doctor or she is a lawyer.
Identify the premises and conclusion of the following argument:

All cats are animals. All animals have four legs. Therefore, all cats have four legs.

Determine whether the following argument is valid or invalid:

If it rains today, then the game will be cancelled. It is raining today. Therefore, the game has been cancelled.

Identify the type of fallacy committed in the following argument:

Every time I wash my car, it rains. Therefore, washing my car causes rain.

Translate the following into English: ~(P ^ Q)
Determine the truth value of the following compound proposition:

(P v Q) ^ (~P)

Use truth tables to determine whether the following two propositions are equivalent:

P -> Q and ~Q -> ~P

Identify the type of inference used in the following example:

All birds have feathers. Penguins are birds. Therefore, penguins have feathers.

Use De Morgan's laws to simplify the following:

~(P v Q)

Translate the following into symbolic logic: All dogs bark, but not all dogs bite.

Good Luck!

Sample Logic Problem

Given the following statement:

All cats are animals

Determine if the statement is a valid logical statement.

Step 1: Determine if the statement is a universal statement. In this case, it is a universal statement as it is making a claim about all cats.

Step 2: Determine if the statement is true or false. In this case, it is true that all cats are animals.

Step 3: Determine if the statement is logically valid. In this case, the statement is logically valid because it is true that all cats are animals.

Practice Problems

Given the following statement:

Some dogs are mammals

Determine if the statement is a valid logical statement.

Given the following statement:

All birds can fly

Determine if the statement is a valid logical statement.

Given the following statement:

No cats are dogs

Determine if the statement is a valid logical statement.

Given the following statement:

Some cats are not animals

Determine if the statement is a valid logical statement.

Given the following statement:

All mammals are animals

Determine if the statement is a valid logical statement.

Logic Practice Sheet

Boolean Algebra

What is the definition of a Boolean expression?
What is the difference between a conjunction and a disjunction?
How is the logical OR operator represented in Boolean algebra?
How is the logical NOT operator represented in Boolean algebra?
What is the De Morgan's theorem?

Predicate Logic

What is the difference between a universal and an existential statement?
What is a quantifier?
How is the logical AND operator represented in predicate logic?
How is the logical OR operator represented in predicate logic?
What is the difference between a tautology and a contradiction?

Proofs

What is the difference between a direct and an indirect proof?
How do you prove a statement by contradiction?
How do you prove a statement using the method of exhaustion?
What is a proof by induction?
How do you use the method of contrapositive to prove a statement?

Here's some sample Logic quizzes Sign in to generate your own quiz worksheet.

Problem	Answer
What is the difference between a deductive argument and an inductive argument?	A deductive argument is one in which it is impossible for the premises to be true but the conclusion false, while an inductive argument is one in which the conclusion is probabilistic based on the premises.
What is a valid argument?	A valid argument is an argument in which the conclusion necessarily follows from the premises, and where the premises are true, the conclusion must be true as well.
What is an argument from analogy?	An argument from analogy is an inductive argument that suggests two things are similar in some way, thus they are likely to be similar in another way as well.
What is a syllogism?	A syllogism is a form of deductive reasoning consisting of two premises and a conclusion that must be true if the premises are true.
What is the difference between a valid argument and a sound argument?	A valid argument is one in which the conclusion necessarily follows from the premises, whereas a sound argument is a valid argument with premises that are actually true.
What is an argument?	An argument is a set of statements or propositions that are used to persuade someone to accept a claim or conclusion.
What is the difference between an enthymeme and a syllogism?	An enthymeme is a syllogism with one premise left unstated, whereas a syllogism consists of two premises and a conclusion which necessarily follows.
What is the difference between necessary and sufficient conditions?	A necessary condition is one that must be present in order for something else to occur, while a sufficient condition is one that, if present, guarantees that something else occurs.
What is a valid form of an argument?	A valid form of an argument is one in which the conclusion necessarily follows from the premises, regardless of the actual content of the premises.
What is a counterexample?	A counterexample is a specific instance or example that refutes or disproves a general claim or statement.

Problem	Answer
What is the definition of Logic?	Logic is the study of valid reasoning, the principles of correct inference, and the criteria for determining whether an argument is sound or valid.
What is the law of non-contradiction?	The law of non-contradiction states that a statement and its opposite cannot both be true at the same time.
What is the difference between deductive and inductive reasoning?	Deductive reasoning is a form of logical reasoning in which a conclusion is drawn from a set of premises that are assumed to be true. Inductive reasoning is a form of logical reasoning in which a conclusion is drawn from a set of premises that are assumed to be likely to be true.
What is the difference between a valid argument and a sound argument?	A valid argument is an argument in which the conclusion follows logically from the premises. A sound argument is an argument that is both valid and has true premises.
What is an informal fallacy?	An informal fallacy is an argument that is logically unsound due to a flaw in its structure or content.
What is a formal fallacy?	A formal fallacy is an argument that is logically unsound due to a flaw in its form.
What is the difference between a categorical and a conditional statement?	A categorical statement is a statement that makes a claim about all members of a certain category. A conditional statement is a statement that makes a claim about a particular situation that is contingent upon certain conditions being met.
What is the difference between a valid argument and an invalid argument?	A valid argument is an argument in which the conclusion follows logically from the premises. An invalid argument is an argument in which the conclusion does not follow logically from the premises.
What is a syllogism?	A syllogism is a type of logical argument consisting of two premises and a conclusion. The premises are used to draw a conclusion based on the logical relationship between the premises.
What is the difference between an a priori and an a posteriori argument?	An a priori argument is an argument based on logical reasoning and does not require any empirical evidence. An a posteriori argument is an argument based on empirical evidence and does not require any logical reasoning.

Logic Quiz

Question	Answer
What is an argument in logic?	An argument in logic is a set of statements, one of which is the conclusion, and the other is the premise or premises which are used to support the conclusion.
What is the purpose of logic?	The purpose of logic is to enable us to distinguish between valid and invalid arguments and to identify valid arguments.
What is the law of non-contradiction?	The law of non-contradiction states that a proposition and its negation cannot both be true at the same time.
What is a logical fallacy?	A logical fallacy is an error in reasoning that results in an invalid argument.
What is an example of a logical fallacy?	An example of a logical fallacy is the appeal to emotion, which is an argument that uses emotion rather than reason to try to persuade the audience.
What is the difference between a valid argument and an invalid argument?	A valid argument is one in which the premises logically guarantee the truth of the conclusion. An invalid argument is one in which the premises do not logically guarantee the truth of the conclusion.
What is the difference between deduction and induction?	Deduction is a form of reasoning in which a conclusion is drawn from premises that are assumed to be true. Induction is a form of reasoning in which a general conclusion is drawn from specific examples.
What is a syllogism?	A syllogism is a type of logical argument consisting of three parts: two premises and a conclusion.
What is an example of a syllogism?	An example of a syllogism is: All cats are mammals. All mammals are animals. Therefore, all cats are animals.
What is the difference between a necessary truth and a contingent truth?	A necessary truth is a statement that is true in all possible worlds. A contingent truth is a statement that is true in some possible worlds but not in all.