Find the minterm expansion of f(P, Q, R) = PQ + QR' + PR'.

 The minterm expansion of $f(P, Q, R) = PQ + QR' + PR'$ is 

(A) $m_2 + m_4 + m_6 + m_7$ 

(B) $m_0 + m_1 + m_3 + m_5$ 

(C) $m_0 + m_1 + m_6 + m_7$ 

(D) $m_2 + m_3 + m_4 +m_5$ 

(GATE 2010) 

Answer: (A) $m_2 + m_4 + m_6 + m_7$ 

Explanation: 

$f(P, Q, R)$ 

$= PQ + QR' + PR'$ 

$= PQ(R + R') + (P + P')QR' + P(Q + Q')R'$, since $A + A' = 1$ 

$= PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R'$ 

$= PQR + PQR' + P'QR' + PQ'R'$, since $A + A = A$ 

$= m_7 + m_6 + m_2 + m_4$  

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