Question

 

1.     True or false: (~p∧q) ∨ (~p∨q)≡ (~p∨q)

Answer 1

$\left( \sim p\land q \right) \lor \left( \sim p\lor q \right) =\\=\left( \sim p\lor \sim p\lor q \right) \land \left( q\lor \sim p\lor q \right) =\\=\left( \sim p\lor q \right) \land \left( \sim p\lor q \right) =\sim p\lor q\Rightarrow \\\Rightarrow True$