Math: Logic and Truth Tables Worksheet

Question 1

Let p be true and q be false. Find the truth value of p AND q.

Accepted Answer

The statement p AND q is false because both parts must be true for a conjunction to be true, and q is false.

Question 2

Let p be true and q be false. Find the truth value of p OR q.

Accepted Answer

The statement p OR q is true because at least one part is true, and p is true.

Question 3

Let p be false. Find the truth value of NOT p.

Accepted Answer

The statement NOT p is true because negation reverses the truth value of the original statement.

Question 4

Complete the truth table values for p OR q when the rows are: (T, T), (T, F), (F, T), and (F, F).

Accepted Answer

The truth values are true, true, true, and false. An OR statement is false only when both statements are false.

Question 5

Complete the truth table values for p AND q when the rows are: (T, T), (T, F), (F, T), and (F, F).

Accepted Answer

The truth values are true, false, false, and false. An AND statement is true only when both statements are true.

Question 6

Let p be true and q be true. Find the truth value of NOT (p AND q).

Accepted Answer

The statement NOT (p AND q) is false because p AND q is true, and negating it makes it false.

Question 7

Let p be false and q be true. Find the truth value of NOT p OR q.

Accepted Answer

The statement NOT p OR q is true because NOT p is true and q is also true, so the OR statement is true.

Question 8

For the conditional statement 'If p, then q,' determine the truth value when p is true and q is false.

Accepted Answer

The conditional statement is false because a conditional is only false when the first part is true and the second part is false.

Question 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).

Accepted Answer

The truth values are true, false, true, and true. A conditional is false only when p is true and q is false.

Question 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).

Accepted Answer

The truth values are true, false, false, and true. A biconditional is true when both statements have the same truth value.

Question 11

Let p be false and q be false. Find the truth value of p OR NOT q.

Accepted Answer

The statement p OR NOT q is true because NOT q is true when q is false, and an OR statement with one true part is true.

Question 12

Let p be true and q be false. Find the truth value of (p OR q) AND p.

Accepted Answer

The statement (p OR q) AND p is true because p OR q is true and p is true, so the final AND statement is true.

Question 13

Determine whether the statements 'It is raining' and 'It is not raining' are negations of each other. Explain.

Accepted Answer

Yes, these statements are negations of each other because one statement is true exactly when the other statement is false.

Question 14

Write the negation of the statement: 'The number 12 is even.'

Accepted Answer

The negation is 'The number 12 is not even.' This statement reverses the truth value of the original statement.

Question 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?

Accepted Answer

The matching compound statement is NOT (p OR q). The statement p OR q is false only when both p and q are false, so its negation is true only in that row.

Math: Logic and Truth Tables

Math: Logic and Truth Tables

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