For any two statements p and q, the negation of the expression p [ ] (~p [ ] q) is :

Question

For any two statements p and q, the negation of
the expression

p $$ \vee $$ (~p $$ \wedge $$ q) is :

Accepted Answer

$$ \sim $$[p $$ \vee $$ (~p $$ \wedge $$ q)]

= $$ \sim $$ p $$ \wedge $$ ($$ \sim (\[ \sim $$ p $$ \vee $$ $$ \sim $$q)

= $$ \sim $$ p $$ \wedge $$ ( p $$ \vee $$ $$ \sim $$q)

= ( $$ \sim $$ p $$ \wedge $$ p ) $$ \vee $$ ($$ \sim $$ p $$ \wedge $$ $$ \sim $$q)

= ($$ \sim $$ p $$ \wedge $$ $$ \sim $$q) [ as $$ \sim $$ p $$ \wedge $$ p is always false)

Solutions · 1