Let the operations [*, , ].

Question

Let the operations $$*, \odot \in\{\wedge, \vee\}$$. If $$(\mathrm{p} * \mathrm{q}) \odot(\mathrm{p}\, \odot \sim \mathrm{q})$$ is a tautology, then the ordered pair $$(*, \odot)$$ is :

Accepted Answer

$$ * ,\, \odot  \in \{  \wedge ,\, \vee \} $$

Now for $$(p * q) \odot (p \odot  \sim q)$$ is tautology

(A) $$( \vee , \wedge ):(p \vee q) \wedge (p \wedge  \sim q)$$ not a tautology

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

$$ = P \vee T$$ is tautology

(C) $$( \wedge , \wedge ):(p \wedge q) \wedge (p \wedge  \sim q)$$

$$ = (p \wedge p) \wedge (q \wedge  \sim q) = p \wedge F$$ not a tautology (Fallasy)

(D) $$( \wedge , \vee ):(p \wedge q) \vee (p \vee  \sim q)$$ not a tautology

Solutions · 1