If p \[ \to \] (\[ \sim \] p\[ \vee \] \[ \sim \] q) is false, then the truth values of p and q are respectively :
Solutions · 1
Official solution
p
q
~p
~q
~p \[ \vee \] ~q
p \[ \to \] (~p \[\vee\] ~q)
T
T
F
F
F
F
T
F
F
T
T
T
F
T
T
F
T
T
F
F
T
T
T
T
From the truth table,
p \[ \to \] (~p \[\vee\] ~q) is false only when p and q both are true.