Simplify the given boolean expression F=P.Q'.R(Q.S+R.S.T) + P.R'
Answers
F(P, Q, R, S) = PQ + P'QR + P'QR'S
= Q(P + P'R + P'R'S)
= Q(P + R + R'S)
= Q(P + R + S)
= PQ + QR + QS
hope it helps you !!
Your question is incomplete. Please refer to the content below:
Simplify the given Boolean expression:
F: F(P, Q, R, S) = PQ + P'QR + P'QR'S
Concept:
A Boolean expression:
It refers to a logical statement that is either true or false.
Given:
We are given the expression:
F: F(P, Q, R, S) = PQ + P'QR + P'QR'S
Find:
We need to simplify the expression.
Solution:
We have:
F: F(P, Q, R, S) = PQ + P'QR + P'QR'S
F = PQ + P'Q( R + R'S )
This can also be written as:
F = PQ + P'Q( R + R' )( R + S )
F = PQ + P'Q( R + S )
F = Q ( P + P'R + P'S )
F = Q [ ( P + P')(P + R) + ( P + P')(P + S) ]
F = Q( P + R + P + S)
According to the Boolean algebra, we get that:
F = Q ( P + R + S)
F = QP + QR + QS
Therefore, after simplifying the expression F: F(P, Q, R, S) = PQ + P'QR + P'QR'S, we get the answer as QP + QR + QS.
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