Number of Functions from A into B
Question:
If \( A=\{1,2,3\} \), \( B=\{x,y\} \), then the number of functions that can be defined from \(A\) into \(B\) is
(a) \(12\)
(b) \(8\)
(c) \(6\)
(d) \(3\)
Solution:
Number of functions from a set having \(m\) elements to a set having \(n\) elements is
\[ n^m \]
Here,
\[ m=3,\qquad n=2 \]
Therefore,
\[ 2^3=8 \]
\[ \boxed{\text{Correct Answer: (b)}} \]