01 Key Concepts
Propositions
A statement that is either true or false, but not both, such as 'It is raining' or '2+2=4'.
Logical 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).
Implication (if...then)
'P implies Q' is false only when P is true and Q is false; in every other case, it's true.
Biconditional (if and only if)
'P iff Q' is true exactly when P and Q have the same truth value (both true or both false).
Truth 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.
02 Solved Examples
Example 1 Construct the truth table for P AND Q.
- List all combinations of P and Q: (T,T), (T,F), (F,T), (F,F).
- P AND Q is true only when both are true.
Answer: T AND T = T; T AND F = F; F AND T = F; F AND F = F
Example 2 Construct the truth table for P OR Q.
- List all combinations of P and Q.
- P OR Q is true whenever at least one of them is true.
Answer: T OR T = T; T OR F = T; F OR T = T; F OR F = F
Example 3 Evaluate 'P implies Q' when P is true and Q is false.
- Implication is false only in the one case where P is true and Q is false.
- This is exactly that case.
Answer: False
03 Practice Questions
1Evaluate NOT(True).
False
2Evaluate True AND False.
False
3Evaluate False OR True.
True
4Evaluate 'P implies Q' when P is false and Q is true.
True (implication is only false when P is true and Q is false)
5Evaluate 'P iff Q' when both P and Q are false.
True
📄 Logic — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.