Let # be a binary operator defined as 𝑋 # π‘Œ = 𝑋′ + π‘Œβ€² where 𝑋 and π‘Œ are…

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

Let # be a binary operator defined as

𝑋 # π‘Œ = 𝑋′ + π‘Œβ€² where 𝑋 and π‘Œ are Boolean variables.

Consider the following two statements.

(S1) (𝑃 # 𝑄)#𝑅 = 𝑃#(𝑄 # 𝑅)

(S2) 𝑄#𝑅 = 𝑅#𝑄

Which of the following is/are true for the Boolean variables 𝑃, 𝑄 and 𝑅?

  1. A.

    Only S1 is true

  2. B.

    Only S2 is true

  3. C.

    Both S1 and S2 are true

  4. D.

    Neither S1 nor S2 are true

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