#### Question

The negation of p ∧ (q → r) is

- p ∨ (~q ∨ r)
- ~p ∧ (q → r)
- ~p ∧ (~q → ~r)
- ~p ∨ (q ∧ ~r)

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#### Solution

(d)

~ [P ∧ (q → r) =~[( P)] ∨ [~ (q → r)] .................By De Morgan's law

=~[( P)] ∨ [~ (~q ∨ r )]...............By Conditional Law

=~[( P)] ∨ [( q ∧ ~r )]...................By De Morgan's law

~ [P ∧ (q → r)]= ~ P ∨ (q ∧ ~r)

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Solution for question: The negation of p ∧ (q → r) is concept: null - Algebra of Statements. For the courses HSC Science (General) , HSC Science (Computer Science), HSC Science (Electronics), HSC Arts, HSC Commerce (Marketing and Salesmanship), HSC Commerce