Please dont handwrite. I have trouble reading. Thank you very much….

Please dont handwrite. I have trouble reading. Thank you very much.

Problem 4 (12 points): The exclusive-or operator ⊕, is defined by the rule that a ⊕ b is true whenever a or b is true but not both.

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Calculate x ⊕ x, x ⊕ ¬x, x ⊕ 1, x ⊕ 0.

Prove or disprove that x + (y ⊕ z) = (x + y) ⊕ (x + z)

Prove or disprove that x ⊕ (y + z) = (x ⊕ y) + (x ⊕ z)

Expert Answer

answers

SOLUTION:-

(1) Calculate x ⊕ x, x ⊕ ¬x, x ⊕ 1, x ⊕ 0.

Solution: x ⊕ x = 0

x ⊕ ¬x = 1

x ⊕ 1 = ¬x

x ⊕ 0 = x

(2) Prove or disprove that x + (y ⊕ z) = (x + y) ⊕ (x + z)

Solution:

It is not TRUE , if we assume that x is true then x + (y ⊕ z) will be true always although (x + y) ⊕ (x + z) will be FALSE always.

(3) Prove or disprove that x ⊕ (y + z) = (x ⊕ y) + (x ⊕ z)

Solution:

It is not TRUE , if we assume that x is true then x ⊕ (y + z) will be equal to ¬(y + z) , that means neither of y, z, and (x ⊕ y) + (x ⊕ z) is equal to (¬y) ∨ (¬z) , it means nand of y and z. So finally we can say that they are absolutely not identical.

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