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The minterm expansion of f (P, Q, R) = PQ + QR̅ + PR̅ is
- a)m2 + m4 + m6 + m7
- b)m0 + m1 + m6 + m7
- c)m2 + m3 + m4 + m5
- d)m0 + m1 + m3 + m7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 +...
F(P, Q, R) = PQ + QR' + PR'
= PQ (R + R') + (P + P')QR' + P(Q + Q')R'
= PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R'
= PQR + PQR' + P'QR' + PQ'R'
= m7 + m6 + m2 + m4
= m2 + m4 + m6 + m7
= PQ (R + R') + (P + P')QR' + P(Q + Q')R'
= PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R'
= PQR + PQR' + P'QR' + PQ'R'
= m7 + m6 + m2 + m4
= m2 + m4 + m6 + m7
Most Upvoted Answer
The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 +...
F(P, Q, R) = PQ + QR' + PR'
= PQ (R + R') + (P + P')QR' + P(Q + Q')R'
= PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R'
= PQR + PQR' + P'QR' + PQ'R'
= m7 + m6 + m2 + m4
= m2 + m4 + m6 + m7
= PQ (R + R') + (P + P')QR' + P(Q + Q')R'
= PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R'
= PQR + PQR' + P'QR' + PQ'R'
= m7 + m6 + m2 + m4
= m2 + m4 + m6 + m7
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Community Answer
The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 +...
To find the minterm expansion of the given function f(P, Q, R) = PQ QR PR, we need to identify the minterms where the function evaluates to 1.
A minterm is a product term that includes all the input variables of a function in either their true or complemented form. In this case, we have three input variables P, Q, and R.
PQ QR PR is the product of three minterms, one for each input variable. To determine the minterms where the function evaluates to 1, we need to consider all possible combinations of P, Q, and R that satisfy the given function.
Let's consider each minterm separately:
1. PQ: This minterm is true when P is true and Q is true. So, the minterm PQ evaluates to 1 when P = 1 and Q = 1.
2. QR: This minterm is true when Q is true and R is true. So, the minterm QR evaluates to 1 when Q = 1 and R = 1.
3. PR: This minterm is true when P is true and R is true. So, the minterm PR evaluates to 1 when P = 1 and R = 1.
Therefore, the minterm expansion of f(P, Q, R) = PQ QR PR is given by the combinations where PQ, QR, and PR are true.
Now, let's identify the minterms where the function evaluates to 1:
- m2: P = 1, Q = 0, R = 1 (PR = 1)
- m4: P = 1, Q = 1, R = 0 (PQ = 1)
- m6: P = 1, Q = 1, R = 1 (PQ = 1, QR = 1, PR = 1)
- m7: P = 1, Q = 1, R = 1 (PQ = 1, QR = 1, PR = 1)
Therefore, the minterm expansion of f(P, Q, R) = PQ QR PR is m2 m4 m6 m7, which corresponds to option A.
A minterm is a product term that includes all the input variables of a function in either their true or complemented form. In this case, we have three input variables P, Q, and R.
PQ QR PR is the product of three minterms, one for each input variable. To determine the minterms where the function evaluates to 1, we need to consider all possible combinations of P, Q, and R that satisfy the given function.
Let's consider each minterm separately:
1. PQ: This minterm is true when P is true and Q is true. So, the minterm PQ evaluates to 1 when P = 1 and Q = 1.
2. QR: This minterm is true when Q is true and R is true. So, the minterm QR evaluates to 1 when Q = 1 and R = 1.
3. PR: This minterm is true when P is true and R is true. So, the minterm PR evaluates to 1 when P = 1 and R = 1.
Therefore, the minterm expansion of f(P, Q, R) = PQ QR PR is given by the combinations where PQ, QR, and PR are true.
Now, let's identify the minterms where the function evaluates to 1:
- m2: P = 1, Q = 0, R = 1 (PR = 1)
- m4: P = 1, Q = 1, R = 0 (PQ = 1)
- m6: P = 1, Q = 1, R = 1 (PQ = 1, QR = 1, PR = 1)
- m7: P = 1, Q = 1, R = 1 (PQ = 1, QR = 1, PR = 1)
Therefore, the minterm expansion of f(P, Q, R) = PQ QR PR is m2 m4 m6 m7, which corresponds to option A.
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The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer?.
The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minterm expansion of f (P, Q, R) = PQ + QR + PR isa)m2 + m4 + m6 + m7b)m0 + m1 + m6 + m7c)m2 + m3 + m4 + m5d)m0 + m1 + m3 + m7Correct answer is option 'A'. Can you explain this answer?.
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