Let \(A = \{1, 2, 3\}\) and \(B = \{x, y\}\).
Match List-I with List-II
| List-I | List-II | ||
| (A) | Number of functions from A to B | (I) | 6 |
| (B) | Number of one-one functions from A to B | (II) | 64 |
| (C) | Number of onto functions from A to B | (III) | 0 |
| (D) | Number of relations from A to B | (IV) | 8 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(A) Number of functions from A to B
This matches (IV) 8.
Each of the 3 elements of A has 2 possible images:
\(2 \times 2 \times 2 = 8\)
(B) Number of one-one functions from A to B
This matches (III) 0.
A one-one function needs 3 different images, but B has only 2 elements. So no one-one function exists.
(C) Number of onto functions from A to B
This matches (I) 6.
Of the 8 functions, only two are not onto: all of A sent to x, and all of A sent to y.
\(8 - 2 = 6\)
(D) Number of relations from A to B
This matches (II) 64.
A relation from A to B is any subset of \(A \times B\), which has \(3 \times 2 = 6\) elements:
\(2^{6} = 64\)