The Boolean expression - p q - - p q is equivalent to

∼ (p q) ∨ (∼ p q) Using Set Theory approach, above statement can be expressed as nbsp; (P ∪ Q)^c ∪ (P^c ∩ Q) =(P^c ∩ Q^c) ∪ (P^c ∩ Q) =P^c ∩ (Q^c ∪ Q) =P^c ...

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Standard XII

Mathematics

Validation of Statement

The Boolean e...

Question

The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to

\sim p

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\sim q

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p

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q

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Solution

The correct option is A $\sim p$
$\sim (p \lor q) \lor (\sim p \land q)$
Using Set Theory approach, above statement can be expressed as
$(P \cup Q)^{c} \cup (P^{c} \cap Q)$
$= (P^{c} \cap Q^{c}) \cup (P^{c} \cap Q)$
$= P^{c} \cap (Q^{c} \cup Q)$
$= P^{c} \cap U$
$= P^{c}$

Hence, the answer is $\sim p$

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The Boolean expression ∼ (p∨q)∨(∼ p∧q) is equivalent to

The correct option is A ∼ p∼ (p∨q)∨(∼ p∧q) Using Set Theory approach, above statement can be expressed as (P∪Q)c∪(Pc∩Q) =(Pc∩Qc)∪(Pc∩Q) =Pc∩(Qc∪Q) =Pc∩U =Pc Hence, the answer is ∼p

The Boolean expression $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to