The minterm expansion of \(f(P, Q, R) = PQ + Q \overline R + P \overline R\) is
2010
The minterm expansion of \(f(P, Q, R) = PQ + Q \overline R + P \overline R\) 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.
\( m_2 + m_3 + m_4 + m_5\)
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Correct answer: A
Key idea: evaluate the function separately for R = 0 and R = 1 to find which input combinations make it 1.
If R = 0 (so R' = 1): f = PQ + Q·1 + P·1 = PQ + Q + P = P + Q. Thus f = 1 for any combination with P = 1 or Q = 1, giving 010 (m2), 100 (m4), and 110 (m6).
If R = 1 (so R' = 0): f = PQ + 0 + 0 = PQ. Thus f = 1 only for 111 (m7).
Therefore f(P, Q, R) = m2 + m4 + m6 + m7.
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