Match List I with List II \(\begin{array}{|c|l|c|l|l|} \hline \text{List I} &…
2021
Match List I with List II
\(\begin{array}{|c|l|c|l|l|} \hline \text{List I} & \text{List II} \\ \hline \text{Identity} & \text{Name} \\ \hline \text{A. x + x =x} & \text{I. Identity Law} \\ \hline \text{B. x + 0 = x} & \text{II. Absorption Law} \\ \hline \text{C. x +1 = 1} & \text{III. Idempotent law} \\ \hline \text{D. x + xy = x} & \text{IV. Domination Law} \\ \hline \end{array}\)
Choose the correct answer from the options given below:
- A.
A ‐ III, B ‐I , C ‐ II, D ‐ IV
- B.
A ‐ I, B ‐III , C ‐ IV, D ‐ II
- C.
A ‐ III, B ‐I , C ‐ IV, D ‐ II
- D.
A ‐ III, B ‐IV , C ‐ I, D ‐ II
Attempted by 341 students.
Show answer & explanation
Correct answer: C
Correct matching and brief explanations:
x + x = x — Idempotent law. Explanation: OR-ing a value with itself gives the same value.
x + 0 = x — Identity law. Explanation: 0 is the additive identity for OR, so it does not change x.
x + 1 = 1 — Domination law. Explanation: 1 dominates in OR, so x OR 1 equals 1 regardless of x.
x + x y = x — Absorption law. Explanation: x OR (x AND y) simplifies to x because x already guarantees the result.
Quick check: Substitute x = 0 and x = 1 in each identity to verify they hold for both possible values.