Math  /  Discrete

QuestionDetermine the truth value of the statement (pq)r(p \wedge q) \vee \sim r using the following conditions. a) pp is false, qq is true, and rr is true. b) pp is false, qq is false, and rr is false. a) If pp is false, qq is true, and rr is true, what is the value of (pq)r(p \wedge q) \vee \sim r ? False True b) If pp is false, qq is false, and rr is false, what is the value of (pq)r(p \wedge q) \vee \sim r ? True False

Studdy Solution
Evaluate the expression (pq)r(p \wedge q) \vee \sim r for condition (b): pp is false, qq is false, and rr is false.
2.1 Evaluate pqp \wedge q: - Since both pp and qq are false, pqp \wedge q is false.
2.2 Evaluate r\sim r: - Since rr is false, r\sim r is true because NOT false is true.
2.3 Evaluate (pq)r(p \wedge q) \vee \sim r: - Since pqp \wedge q is false and r\sim r is true, (pq)r(p \wedge q) \vee \sim r is true because at least one condition is true for the OR operation to be true.
The truth values are: a) False b) True

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord