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Question: Answered & Verified by Expert
Let $A=\{x, y, z\}$ and $B=\{p, q, r, s\} .$ What is the number of distinct relations from B to A?
MathematicsPermutation CombinationNDANDA 2015 (Phase 1)
Options:
  • A 4096
  • B 4094
  • C 128
  • D 126
Solution:
1063 Upvotes Verified Answer
The correct answer is: 4096
$\mathrm{A}=\{\mathrm{x}, \mathrm{y}, \mathrm{z}\}$
$\mathrm{B}=(\mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s})$
$\mathrm{n}(\mathrm{A})=3$
$\mathrm{n}(\mathrm{B})=4$
Number of distinct relations $=2^{n(A) \times n(B)}=2^{3 \times 4}=2^{12}=4096$
$\therefore$ option (a) is correct.

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