Match the LIST-I with LIST-II LIST-I (Boolean Algebra Law) A. Absorption Law…
2025
Match the LIST-I with LIST-II
LIST-I (Boolean Algebra Law)
A. Absorption Law
B. Bounded Law
C. Identity Law
D. Distributive Law
LIST-II (Axioms)
I. a + 1 = 1
II. a + 0 = a
III. a * (b + c) = (ab) + (ac)
IV. a + (a * b) = a
Choose the correct answer from the options given below:
- A.
A-IV, B-I, C-II, D-III
- B.
A-IV, B-III, C-I, D-II
- C.
A-III, B-IV, C-II, D-I
- D.
A-II, B-III, C-IV, D-I
Attempted by 1516 students.
Show answer & explanation
Correct answer: A
Concept: Boolean algebra names a fixed set of postulates for how AND/OR combine with a variable and the constants 0/1: the Identity Law names the element that leaves a variable unchanged (a+0=a, a·1=a); the Bounded (also called Boundedness/Annulment/Universal-Bound) Law names the element that dominates regardless of the variable (a+1=1, a·0=0); the Absorption Law names the case where a compound term is absorbed into the simpler term it already contains (a+(a·b)=a); and the Distributive Law names AND distributing over OR exactly as multiplication distributes over addition (a·(b+c)=(a·b)+(a·c)). Matching a law’s name to its symbolic form is matching this fixed vocabulary.
Application: matching each law to its axiom
List-I item | Matches | Why |
|---|---|---|
A. Absorption Law | IV. a+(a·b)=a | the compound term a·b is absorbed into a |
B. Bounded Law | I. a+1=1 | ORing with 1 dominates to 1 regardless of a |
C. Identity Law | II. a+0=a | 0 is OR’s identity element; it leaves a unchanged |
D. Distributive Law | III. a·(b+c)=(ab)+(ac) | AND distributes over OR, like × over + in ordinary algebra |
Cross-check: each of the four axioms I–IV is used exactly once across A–D, so A-IV, B-I, C-II, D-III is a complete one-to-one correspondence. The Bounded Law’s AND-side dual, a·0=0, is also consistent with treating I as the “domination/boundary” identity rather than the Identity Law’s a·1=a — confirming B is not C. Some sources label a+1=1, a·0=0 the Boundedness Law, Universal Bound Law, Null Law, Dominance Law, or Annulment Law; all refer to the same identity as “Bounded Law” here.
Contrasting the other pairings:
A-IV, B-III, C-I, D-II sets Distributive Law’s formula (III) against Bounded Law, and Bounded Law’s own formula (I) against Identity Law — it cross-swaps B, C and D.
A-III, B-IV, C-II, D-I sets Distributive Law’s formula (III) against Absorption Law, and Absorption Law’s own formula (IV) against Bounded Law — it swaps A and B, and separately swaps D away from III.
A-II, B-III, C-IV, D-I sets Identity Law’s formula (II) against Absorption Law, Distributive Law’s formula (III) against Bounded Law, and Absorption Law’s formula (IV) against Identity Law — three of the four assignments are shifted.
Result: the correct pairing is A-IV, B-I, C-II, D-III.
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