Gate2019 cs Q16
0. Which one of the following is NOT a valid identity?
- Option : B
- Explanation : (a) x ⊕ y = (xy + x′y ′)′ = (xy )′ = x ⊕ y, it is valid. (b) (x + y) ⊕ z = (x + y).z + (x + y)z = xyz + xz + yz = 1 4,6 2,6 = Σm(1, 2, 4, 6) (x + y) ⊕ z = x(y+z) + x (y+z) = xy + xz + yz = 2,3 1,3 4 = Σm(1, 2, 3, 4) (x + y) ⊕ z ≠ x ⊕ (y + z) So option (b) is invalid. (c) (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z) Associativity is true on Ex-OR operator so it valid. (d) x ⊕ y = (x + y)(x + (y) = (x + y)xy = (x + y)x0 = (x + y), so it is valid.
