The negation of the statement [((A (B C)) (A B)) A] is

Question

The negation of the statement $$((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$$ is

Accepted Answer

$$((A \wedge(B \vee C)) \Rightarrow(A \vee B)) \Rightarrow A$$

$$ \equiv $$ $$
[\sim(\mathrm{A} \wedge(\mathrm{B} \vee \mathrm{C})) \vee(\mathrm{A} \vee \mathrm{B})] \Rightarrow \mathrm{A}
$$

$$ \equiv $$ $$
\sim(\sim(A \wedge(B \vee C)) \vee(A \vee B)) \vee A
$$

$$ \equiv $$ $$
(A \wedge(B \vee C)) \wedge \sim(A \vee B) \vee A
$$

$$ \equiv $$ $$
(f \vee A)=A
$$

$$
\therefore \text { Negation of statement }=\sim A
$$

Solutions · 1