Question

Minimize: F =PQ +(PR)' + PQ'R using Boolean laws.​

Answer 1

Minimization of F =PQ +(PR)' + PQ'R using Boolean laws.​

• Given,
• F =PQ +(PR)' + PQ'R
• F = PQ (R+R') +(PR)' + PQ'R           (∵ R+R' = 1)
• F = PQR + PQR' +(PR)' + PQ'R
• F = PR (Q+Q') + PQR' + (PR)'
• F = PR + PQR' +(PR)'
• F = 1 + PQR'         [∵ PR + (PR)' = 1]
• ∴ F = 1 + PQR'

Answer 2

The correct answer will be "$1+PQ\bar{R}$". The further description is given below.

Explanation:

The given equation is:

$F=PQ+{PR}'+P{Q}'R$

On applying Boolean laws, we get

⇒  $F=PQ+\bar{PR}+P\bar{Q}R$

        $=PQ(R+\bar{R})+\bar{PR}+P\bar{Q}R$

∴ ($a+\bar{a}=1$)

       $=PQR+PQ\bar{R}+P\bar{R}+P\bar{Q}R$

       $=PR(Q+\bar{Q})+PQ\bar{R}+\bar{PR}$

       $=PR+\bar{PR}+PQ\bar{R}$

       $=1+PQ\bar{R}$

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