The statement [B ( ( A ) B )] is equivalent to :

Question

The statement $$B \Rightarrow \left( {\left( { \sim A} \right) \vee B} \right)$$ is equivalent to :

Accepted Answer

$$A \to (B \to A)$$

$$ \Rightarrow A \to ( \sim B \vee A)$$

$$ \Rightarrow \, \sim A \vee ( \sim B \vee A)$$

$$ \Rightarrow \, \sim B \vee ( \sim A \vee A)$$

$$ \Rightarrow \, \sim B \vee t$$

= t (tantology)

From options :

(B) $$A \to (A \vee B)$$

$$ \Rightarrow \, \sim A \vee (A \vee B)$$

$$ \Rightarrow ( \sim A \vee A) \vee B$$

$$ \Rightarrow t \vee B$$

$$ \Rightarrow t$$

Solutions · 1