Propositional Logic
PROPOSITIONAL LOGIC is the mathematical study of true/false statements. A PROPOSITION is any statement that is either TRUE or FALSE (not both). "It is raining." (T or F.) "2 + 2 = 4." (T.) "All cats are blue." (F.) Things like "Hello!" or "What time is it?" are NOT propositions — they have no truth value.
Logical connectives. AND (∧): "P and Q" is true ONLY when both are true. OR (∨): "P or Q" is true when AT LEAST ONE is true. NOT (¬): "not P" flips P's truth. IMPLIES (→): "if P then Q" is true unless P is true AND Q is false. EQUIVALENT (↔): "P if and only if Q" — both true or both false. With these 5 operators, you can combine any propositions into complex logical statements.
P = "It is raining" (true). Q = "I have an umbrella" (false). What is the value of "P AND Q"?
TRUTH TABLES make this concrete. For each combination of inputs (T/T, T/F, F/T, F/F), the output is computed. AND truth table: T-T → T, T-F → F, F-T → F, F-F → F. OR: T-T → T, T-F → T, F-T → T, F-F → F. Programmers use these every day — every IF statement is propositional logic. Computers are just very fast logic engines.
Build a Truth Table
Build a truth table for "P AND (NOT Q)." Enumerate: P=T,Q=T; P=T,Q=F; P=F,Q=T; P=F,Q=F. Compute (NOT Q) first, then AND with P. (Hint: result is true only when P is true and Q is false.)
Propositional logic is one of math's most fundamental tools. Computers, mathematics, philosophy, and even some legal arguments rest on it. Mastering it sharpens every other kind of thinking.
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