If the Boolean expression [(p q) (p q)] is a tautology, then [ ] and [ ] are respectively …

Question

If the Boolean expression $$(p \wedge q) \odot (p \otimes q)$$ is a tautology, then $$ \odot $$ and $$ \otimes $$ are respectively given by :

Accepted Answer

$$(p \wedge q)\, \to \,(p \to q)$$

$$(p \wedge q)\, \to \,( \sim p \vee q)$$

$$( \sim p \vee  \sim q)\, \vee ( \sim p \vee q)$$

$$ \sim p \vee ( \sim q \vee q) \Rightarrow $$ Tautology

$$ \Rightarrow  \odot  \Rightarrow  \to $$

$$ \otimes  \Rightarrow  \to $$

Solutions · 1