Let [] [] [], [], [], [] be such that (p [] q) [] ((p [] q) [] q) is a tautology.

Question

Let $$\Delta$$ $$\in$$ {$$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$} be such that (p $$\wedge$$ q) $$\Delta$$ ((p $$\vee$$ q) $$\Rightarrow$$ q) is a tautology. Then $$\Delta$$ is equal to :

Accepted Answer

$(p \vee q) \Rightarrow q$

$$
\begin{aligned}
& \sim(p \vee q) \vee q \\
& =(\sim p \wedge \sim q) \vee q \\
& =(\sim p \vee q) \wedge(\sim q \vee q) \\
& =(\sim p \vee q) \wedge T \\
& =\sim p \vee q
\end{aligned}
$$

Now $(p \wedge q) \Delta(\sim p \vee q)$

$$
\[\begin{array}{cccccc} p & q & \sim p & p \wedge q & \sim p \vee q & (p \wedge q) \Delta(\sim p \vee q) \ T & T & F & T & T & T \ T & F & F & F & F & T \ F & T & T & F & T & T \ F & F & T & F & T & T \end{array}$$
\]

$\therefore \Delta=\Rightarrow$

Solutions · 1