How to solve: Truth Tables & Syllogisms
What this category tests
Tests formal propositional logic — mechanically evaluating compound statements built with AND, OR, NOT, XOR, and IF-THEN, and applying standard logical equivalences to simplify them.
Where this typology comes from
Charles Sanders Peirce worked out early truth-functional analyses in the 1880s-90s, but the row-by-row tabular format familiar today is generally credited to Ludwig Wittgenstein's "Tractatus Logico-Philosophicus" (1921), with logician Emil Post publishing an equivalent method the same year. De Morgan's Laws — the rules for distributing NOT across AND/OR — are named for mathematician Augustus De Morgan, who stated them formally in his 1847 book "Formal Logic."
How to approach it
Build the table systematically, evaluating the innermost parentheses first and working outward. Memorize the standard equivalences (De Morgan's Laws, double negation, the contrapositive) so you can simplify an expression instead of brute-forcing every row. When a problem gives you the output and asks for the inputs, work backward from that output rather than testing combinations at random.
Worked example
Let P = 'It is raining' and Q = 'The match is postponed.' The statement is: NOT (P AND Q). Given that this statement is FALSE, what must be true?
- P is true and Q is true ✓ Correct answer
- P is true and Q is false
- P is false and Q is false
- P is false and Q is true
Explanation NOT (P AND Q) is false exactly when (P AND Q) is true — and AND is only true when both sides are true. So P must be true and Q must be true.
Practice Truth Tables & Syllogisms
- Truth Tables & Syllogisms I · 12 questions · Difficulty 2 out of 5
- Truth Tables & Syllogisms II · 12 questions · Difficulty 3 out of 5
- Truth Tables III — Reverse Deduction · 12 questions · Difficulty 4 out of 5
- Truth Tables & Syllogisms IV — Rules of Inference · 12 questions · Difficulty 4 out of 5