Math: Logic and Truth Tables
Evaluating statements with logical operators
Math: Logic and Truth Tables
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.
AND statements are only true when both statements are true.
The statement p AND q is false because both parts must be true for a conjunction to be true, and q is false. - 2
Let p be true and q be false. Find the truth value of p OR q.
The statement p OR q is true because at least one part is true, and p is true. - 3
Let p be false. Find the truth value of NOT p.
Negation changes true to false and false to true.
The statement NOT p is true because negation reverses the truth value of the original statement. - 4
Complete the truth table values for p OR q when the rows are: (T, T), (T, F), (F, T), and (F, F).
The truth values are true, true, true, and false. An OR statement is false only when both statements are false. - 5
Complete the truth table values for p AND q when the rows are: (T, T), (T, F), (F, T), and (F, F).
Check whether both values in each row are true.
The truth values are true, false, false, and false. An AND statement is true only when both statements are true. - 6
Let p be true and q be true. Find the truth value of NOT (p AND q).
The statement NOT (p AND q) is false because p AND q is true, and negating it makes it false. - 7
Let p be false and q be true. Find the truth value of NOT p OR q.
Evaluate the negation first, then the OR.
The statement NOT p OR q is true because NOT p is true and q is also true, so the OR statement is true. - 8
For the conditional statement 'If p, then q,' determine the truth value when p is true and q is false.
The conditional statement is false because a conditional is only false when the first part is true and the second part 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).
Only one row makes a conditional false.
The truth values are true, false, true, and true. A conditional is false only when p is true and q is false. - 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).
The truth values are true, false, false, and true. A biconditional is true when both statements have the same truth value. - 11
Let p be false and q be false. Find the truth value of p OR NOT q.
Find NOT q first.
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. - 12
Let p be true and q be false. Find the truth value of (p OR q) AND p.
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. - 13
Determine whether the statements 'It is raining' and 'It is not raining' are negations of each other. Explain.
Negations always have opposite truth values.
Yes, these statements are negations of each other because one statement is true exactly when the other statement is false. - 14
Write the negation of the statement: 'The number 12 is even.'
The negation is 'The number 12 is not even.' This statement reverses the truth value of the original statement. - 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?
First decide when p OR q is false, then negate it.
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.