GATE CS 2015 Set 3 — Question 40
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Digital Logic → Boolean Algebra & Logic Gates → Minterms & Maxterms
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Question
Given the function , where is a function in three Boolean variables and and , consider the following statements.(S1)
(S2)
(S3)
(S4)
Which of the following is true?
(S2)
(S3)
(S4)
Which of the following is true?
Correct answer
(A) (S1)- False, (S2)- True, (S3)- True, (S4)- False
Solution
The function is .
Let's construct the truth table:
(minterm 0)
(minterm 1)
(minterm 2)
(minterm 3)
(maxterm 4)
(maxterm 5)
(maxterm 6)
(minterm 7)The minterms (where ) are . Thus, . Statement (S2) is True.
The maxterms (where ) are . Thus, . Statement (S3) is True.Consequently:
(S1) is False.
(S2) is True.
(S3) is True.
(S4) is False.This corresponds to option (A).
Let's construct the truth table:
(minterm 0)
(minterm 1)
(minterm 2)
(minterm 3)
(maxterm 4)
(maxterm 5)
(maxterm 6)
(minterm 7)The minterms (where ) are . Thus, . Statement (S2) is True.
The maxterms (where ) are . Thus, . Statement (S3) is True.Consequently:
(S1) is False.
(S2) is True.
(S3) is True.
(S4) is False.This corresponds to option (A).
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