The negation of ∼ s ∨ ( ∼ r ∧ s) is equivalent to

Question

The negation of ∼ s ∨ ( ∼ r ∧ s) is equivalent to (A) s ∧ ∼ r  (B) s ∧ ( r∧ ∼ s) (C)  s ∨ ( r ∨ ∼ s) (D)  s ∧ r

Tardigrade Admin · Accepted Answer

∼ S V(∼ r ∧ S) S r ∼ r ∼ r ∧ S ∼ S ∼ S V(∼ r ∧ S) ∼(∼ S V(∼ r ∧ S)) T T F F F F T T F T T F T F F T F F T T F F F T F T T F

S	r	$\sim r$	$\sim r \land S$	$\sim S$	$\sim S V (\sim r \land S)$	$\sim (\sim S V (\sim r \land S))$
T	T	F	F	F	F	T
T	F	T	T	F	T	F
F	T	F	F	T	T	F
F	F	T	F	T	T	F

Q. The negation of $\sim s \lor (\sim r \land s)$ is equivalent to