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Question
The negation of p ∧ (q → r) is ______________.
Options
p ∨ ( ~q ∨ r )
~p ∧ ( q → r )
~p ∧ ( ~q → ~r )
~p ∨ ( q ∧ ~r )
Solution
~ [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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