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Logical Connectives

If the Boolea...

Question

If the Boolean expression $(p \oplus q) \land (\sim p ⊙ q)$ is equivalent to $p \land q$ , where $\oplus, ⊙ \in {\land, \lor}$ , then the ordered pair $(\oplus, ⊙)$ is:

A

(\land, \land)

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B

(\land, \lor)

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C

(\lor, \lor)

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D

(\lor, \land)

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Solution

The correct option is B $(\land, \lor)$
$\begin{matrix} p & q & \sim p & p \lor q & p \land q & \sim p \lor q & \sim p \land q T & T & F & T & T & T & F T & F & F & T & F & F & F F & T & T & T & F & T & T F & F & T & F & F & T & F \end{matrix}$
$\begin{matrix} (p \lor q) \land (\sim p \lor q) & (p \lor q) \land (\sim p \land q) & (p \land q) \land (\sim p \lor q) & (p \land q) \land (\sim p \land q) T & F & T & F F & F & F & F T & T & F & F F & F & F & F \end{matrix}$
From the truth table, we observe that $(p \oplus q) \land (\sim p ⊙ q) = p \land q$

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Logical Connectives

Standard XII Mathematics

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