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Question

# Let A={1,2,3} and B={a,b,c}. If f is a function from A to B and g is a one-one function from A to B, then the maximum number of definitions of

A
f is 9
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B
g is 9
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C
f is 27
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D
g is 6
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Solution

## The correct options are C f is 27 D g is 6For every number in set A there are 3 choices in set B, Hence the total number of functions from A→B are 3×3×3=27.For the first number in set A there are 3 choices in set B,Since the function is one-one the second number in set A has only 2 choices in set B as we can not mapped the two number to the same element. Similarly, the third number has only one choice.Therefore the total number of one one functions from A to B are 3×2×1=6

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