Discrete Mathematics · Quick Reference

Logic Cheat Sheet

Discrete Mathematics · Lesson 1/9

In one line: logic is the study of valid reasoning — the rules that let us combine true and false statements to build sound arguments, and the foundation of how computers make decisions.

Key Ideas

1Propositions. A statement that is either true or false, but not both, such as 'It is raining' or '2+2=4'.

2Logical Connectives. AND (conjunction, true only if both parts are true), OR (disjunction, true if at least one part is true), NOT (negation, flips true/false).

3Implication (if...then). 'P implies Q' is false only when P is true and Q is false; in every other case, it's true.

4Biconditional (if and only if). 'P iff Q' is true exactly when P and Q have the same truth value (both true or both false).

5Truth Tables. A table that lists every possible combination of truth values for the propositions involved, showing the result of a logical expression in each case.

Worked Examples

Construct the truth table for P AND Q.

T AND T = T; T AND F = F; F AND T = F; F AND F = F

Construct the truth table for P OR Q.

T OR T = T; T OR F = T; F OR T = T; F OR F = F

Evaluate 'P implies Q' when P is true and Q is false.

False

Practice Yourself

Evaluate NOT(True).

False

Evaluate True AND False.

False

Evaluate False OR True.

True

Evaluate 'P implies Q' when P is false and Q is true.

True (implication is only false when P is true and Q is false)