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Question

f and h are relations from AB where A={a,b,c,d}; B={s,t,u} defined as follows:
f(a)=t,f(b)=s,f(c)=s,f(d)=u;
h(a)=s,h(b)=t,h(c)=s,h(a)=u,h(d)=u
Which one of the following statement is true?

A
f and h are function
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B
f is a function and h is not a function
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C
f and h are not functions
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D
none of these
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Solution

The correct option is B f is a function and h is not a function
Consider the relation f:AB. For every element of set A there exist a unique element from set B. Hence the relation f:AB is a function.from set A to set B.
Note that for relation h:AB, an element a is mapped to two different elements from set B, namely, s and u. Hence the relation h is not a function.

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