Question #311015

Show that p > q and (p A q) V (-p ^ ¬q are logically equivalent.




1
Expert's answer
2022-03-15T06:34:36-0400

Let us show that pqp ↔q and (pq)(¬p¬q)(p ∧ q) ∨ (¬p ∧ ¬q) are logically equivalent. It follow that


pq=(pq)(qp)=(¬pq)(¬qp)=(¬p¬q)(¬pp)(q¬q)(qp)=(¬p¬q)FF(qp)=(¬p¬q)(pq)=(pq)(¬p¬q)p ↔ q=(p\to q)\land (q\to p) \\=(\neg p\lor q)\land (\neg q\lor p) \\=(\neg p\land\neg q)\lor(\neg p\land p)\lor(q\land\neg q)\lor(q\land p) \\=(\neg p\land\neg q)\lor F\lor F\lor(q\land p) \\=(\neg p\land\neg q)\lor (p\land q) \\= (p\land q)\lor (\neg p\land\neg q)


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS