Meowajdjdj
Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Given the conditional statement ~p -> q which statement is logically equivalent?​

Sagot :

LammettHash

Any implication is logically equivalent to its contrapositive. In other words,

¬p ⇒ q   ⇔   ¬q ⇒ p

(¬ means the same thing as ~, "not")

To prove this: recall that

p ⇒ q   ⇔   ¬p ∨ q

This is because p ⇒ q is true if p is false, or both p and q are true, i.e.

p ⇒ q   ⇔   ¬p ∨ (p ∧ q)

Disjunction (∨ or "or") distributes over conjunction (∧ or "and"), so that

p ⇒ q   ⇔   (¬p ∨ p) ∧ (¬p ∨ q)

but ¬p ∨ p is always true, or a tautology, so we're just left with ¬p ∨ q.

Then

¬p ⇒ q   ⇔   p ∨ q

…   ⇔   q ∨ p

…   ⇔   ¬(¬q) ∨ p

…   ⇔   ¬q ⇒ p

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.