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Question

Let A={1,3,5,7},B={2,4,6,8} and f:AB, then number of function(s) f that can be defined from A to B is

A
12 if i+f(i)<10, i={1,3,5,7}
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B
24 if i+f(i)<10, i={1,3,5,7}
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C
0 if f(i)i>2, i={1,3,5,7}
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D
12 if f(i)i>2, i={1,3,5,7}
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Solution

The correct option is C 0 if f(i)i>2, i={1,3,5,7}
If i+f(i)<10, i={1,3,5,7}
f(1)<9,f(3)<7,f(5)<5,f(7)<3
So, in B={2,4,6,8}
1 has 4 choices
3 has 3 choices
5 has 2 choices
7 has 1 choice
Number of required functions =4321=24

If f(i)i>2, i={1,3,5,7}
f(1)>3,f(3)>5,f(5)>7,f(7)>9
Element 7 in A have no choice in B.
Number of required functions is 0.

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