Question #187560

(¬p→r) ∧ (q ↔p)


1
Expert's answer
2021-05-11T06:41:47-0400

(¬pr)(qp)=(pq)(¬pr)(\lnot p\rightarrow r)\land (q\leftrightarrow p)=(p\leftrightarrow q)\land(\lnot p\rightarrow r)

Now,

(pq)=(pq)(¬p¬q)(p\leftrightarrow q)=(p\land q)\lor (\lnot p\land \lnot q)

(¬pr)=(pr)(\lnot p\rightarrow r)=(p\lor r)

So,

(pq)(¬pr)=(pr)(p¬q)(q¬p)(p\leftrightarrow q)\land(\lnot p\rightarrow r)=(p\lor r)\land (p\lor \lnot q)\land(q\lor \lnot p)


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