Question

if p is true, q is false, and r is true, find the truth value of the statement.
∼ [p → (q ∧ r)]

Answer 1

if u then v is logically the same as ~u or v
if p then (q^r) is logically the same as ~p or (q^r)
~(~p or (q^r)) is logically the same as p and ~(q or r)
we have p is true
since r is true, then q or r is true
so ~(q or r) is false

since both parts weren't true then the statement is false