Exploring Truth Tables in Discrete Mathematics

What is the purpose of a truth table in logic problems?

• To solve algebraic equations

• To determine the truth values of logical expressions

• To graph functions

• To perform statistical analysis

In a truth table, what does the column 'P and Q' represent?

• The negation of Q

• The negation of P

• The logical AND of P and Q

• The logical OR of P and Q

What is the result of 'P and Q' when P is true and Q is false?

• True

• Both true and false

• False

• Undefined

What does the negation symbol in 'not P and Q' indicate?

• It indicates the logical OR

• It indicates the logical AND

• It indicates the opposite truth value

• It indicates equality

In the expression 'if P then not P and Q', what happens if P is false?

• The expression is undefined

• The expression depends on Q

• The expression is always false

• The expression is always true

What additional column is needed for the second example involving P, Q, and R?

• P and R

• Q and R

• Not Q

• Not P

How many rows are needed in the truth table for three variables (P, Q, R)?

• 10

• 8

• 4

• 6

In the expression 'P or not Q', what is the result if P is false and Q is true?

• Both true and false

• Undefined

• False

• True

What is the result of 'P or not Q if and only if R' when P is true, Q is false, and R is true?

• True

• False

• Undefined

• Both true and false

What is the key condition for an 'if and only if' statement to be true?

• Both sides must be false

• At least one side must be false

• At least one side must be true

• Both sides must be true or both sides must be false