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Question

Mathematics Question on validating statements

The negation of p∧(q→∼r)p{\land}(q \to \sim r) is

A

∼p∨(p∧r)\sim p \lor(p\land r)

B

∼p∧(p∧r)\sim p \land (p\land r)

C

p∨(p∨r)p \lor (p\lor r)

D

p∨(q∧r) p \vee (q \wedge r)

Answer

∼p∧(p∧r)\sim p \land (p\land r)

Explanation

Solution

∼(p∧(q→∼r))=∼p∨∼(q→−r)\sim(p \wedge(q \rightarrow \sim r)) =\sim p \vee \sim(q \rightarrow-r)
=∼p∨(q∧∼(∼r))=\sim p \vee(q \wedge \sim(\sim r))
=∼p∨(q∧r)=\sim p \vee(q \wedge r)