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Question

Let A={a,b,c} and B={1,2,3,4}. Then the number of elements in the set C={f:AB | 2f(A) and f is not one–one} is

A
19
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B
19.00
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C
19.0
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Solution

C={f:AB | 2f(A) and f is not one–one}
Case-I: If f(x)=2 xA, then number of function =1.
Case-II : If f(x)=2 for exactly two elements then total number of many-one function.
=3C2×3C1=9
Case-III : If f(x)=2 for exactly one elements then total number of many-one function
=3C1×3C1=9
Total =1+9+9=19

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