Practice using logical statements, connectives, and truth tables to determine when compound statements are true or false.
Read each problem carefully. Complete the truth values or explanation for each logical statement. Show your work in the space provided.
Evaluating statements with logical operators
Math - Grade 9-12
- 1
Let p be true and q be false. Find the truth value of p AND q.
- 2
Let p be true and q be false. Find the truth value of p OR q.
- 3
Let p be false. Find the truth value of NOT p.
- 4
Complete the truth table values for p OR q when the rows are: (T, T), (T, F), (F, T), and (F, F).
- 5
Complete the truth table values for p AND q when the rows are: (T, T), (T, F), (F, T), and (F, F).
- 6
Let p be true and q be true. Find the truth value of NOT (p AND q).
- 7
Let p be false and q be true. Find the truth value of NOT p OR q.
- 8
For the conditional statement 'If p, then q,' determine the truth value when p is true and q is false.
- 9
For the conditional statement 'If p, then q,' determine the truth values for the rows (T, T), (T, F), (F, T), and (F, F).
- 10
For the biconditional statement 'p if and only if q,' determine the truth values for the rows (T, T), (T, F), (F, T), and (F, F).
- 11
Let p be false and q be false. Find the truth value of p OR NOT q.
- 12
Let p be true and q be false. Find the truth value of (p OR q) AND p.
- 13
Determine whether the statements 'It is raining' and 'It is not raining' are negations of each other. Explain.
- 14
Write the negation of the statement: 'The number 12 is even.'
- 15
A statement is true when p is false and q is false, but false in all other rows. Which compound statement matches this truth table: p AND q, p OR q, NOT (p OR q), or p -> q?