Given the function 𝐹 = 𝑃′ + 𝑄𝑅, where 𝐹 is a function in three Boolean…

GATE Β· 2015 Β· CS Β· Set 3 Β· Computer Science & IT

Given the function 𝐹 = 𝑃′ + 𝑄𝑅, where 𝐹 is a function in three Boolean variables 𝑃,𝑄 and 𝑅 and 𝑃′ = ! 𝑃 , consider the following statements.

(S1) 𝐹 = βˆ‘(4, 5, 6)

(S2) 𝐹 = βˆ‘(0, 1, 2, 3, 7)

(S3) 𝐹 = ∏(4, 5, 6)

(S4) 𝐹 = ∏(0, 1, 2, 3, 7)

Which of the following is true?

  1. A.

    (S1)- False, (S2)- True, (S3)- True, (S4)- False

  2. B.

    (S1)- True, (S2)- False, (S3)- False, (S4)- True

  3. C.

    (S1)- False, (S2)- False, (S3)- True, (S4)- True

  4. D.

    (S1)- True, (S2)- True, (S3)- False, (S4)- False

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