Exams › GATE › Technical

Which one of the following is NOT a valid identity?

1. (x ⊕ y) ⊕ z = x ⊕ (y ⊕ z)
2. (x + y) ⊕ z = x ⊕ (y + z)
3. x ⊕ y = x + y, if xy = 0
4. x ⊕ y = (xy + x'y')'

Correct answer: (x + y) ⊕ z = x ⊕ (y + z)

Solution

Option B is incorrect because it misapplies the properties of the XOR operation (⊕) and addition (+). Unlike addition, XOR does not distribute over addition, making this identity invalid.

Related GATE Technical questions

• A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor?
• Which one of the following kinds of derivation is used by LR parsers?
• In 16-bit 2’s complement representation, the decimal number −28 is:
• Let U = {1,2,...,n}. Let A = {(x,X)|x ∈ X, X ⊆ U}. Consider the following two statements on |A|. I. |A| = n2^(n−1) II. |A| = ∑(k=1 to n) k C(n,k) Which of the above statements is/are TRUE?
• If L is a regular language over Σ = {a, b}, which one of the following languages is NOT regular?
• Let X be a square matrix. Consider the following two statements on X. I. X is invertible. II. Determinant of X is non-zero. Which one of the following is TRUE?

⚔️ Practice GATE Technical free + battle 1v1 →