Question #187560

(¬p→r) ∧ (q ↔p)


Expert's answer

(¬p→r)∧(q↔p)=(p↔q)∧(¬p→r)(\lnot p\rightarrow r)\land (q\leftrightarrow p)=(p\leftrightarrow q)\land(\lnot p\rightarrow r)

Now,

(p↔q)=(p∧q)∨(¬p∧¬q)(p\leftrightarrow q)=(p\land q)\lor (\lnot p\land \lnot q)

(¬p→r)=(p∨r)(\lnot p\rightarrow r)=(p\lor r)

So,

(p↔q)∧(¬p→r)=(p∨r)∧(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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