Which of the Following is a Function from A to B?
Let \( A=\{1,2,3\}, \; B=\{2,3,4\} \), then which of the following is a function from \(A\) to \(B\)?
(a) \( \{(1,2),(1,3),(2,3),(3,3)\} \)
(b) \( \{(1,3),(2,4)\} \)
(c) \( \{(1,3),(2,2),(3,3)\} \)
(d) \( \{(1,2),(2,3),(3,2),(3,4)\} \)
A relation is a function if every element of \(A\) has exactly one image in \(B\).
In option (a), element \(1\) has two images \(2\) and \(3\).
Therefore, not a function.
In option (b), element \(3\) has no image.
Therefore, not a function.
In option (c),
\(1 \to 3,\; 2 \to 2,\; 3 \to 3\)
Every element of \(A\) has exactly one image.
Therefore, it is a function.
In option (d), element \(3\) has two images \(2\) and \(4\).
Therefore, not a function.
\[ \boxed{\text{Correct Answer: (c)}} \]