If n(A) = 3 and n(B) = 2, then number of non-empty relations from A to B is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 63
A relation from A to B is any subset of A × B.
\( \displaystyle n(A\times B)=n(A)\cdot n(B)=3\times 2=6 \)
\( \displaystyle \text{Number of subsets of }A\times B=2^6=64 \)
One of these subsets is the empty relation; removing it:
\( \displaystyle 64-1=63 \)
Why the other options are incorrect
Option (1) 64 — Incorrect. 64 counts all relations, including the empty relation, which the question excludes.
Option (3) 6 — Incorrect. 6 is the number of ordered pairs in A × B, not the number of relations.
Option (4) 8 — Incorrect. 8 = 23 uses only n(A) = 3 instead of the 6 elements of A × B.
Tip: Number of relations from A to B = 2mn; subtract 1 when the question asks for non-empty relations.