Question

Question 11 Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b∈Z}. Is f a function from Z to Z: justify your answer.

Class X1 - Maths -Relations and Functions Page 47

Answer 1

Here,
f = {ab,(a+b)}:a,b∈Z}
Let we take a = 0, b=1 then, ab =0 and (a +b) = 0 + 1 = 1 then, (0,1)∈f

Again, we take a =0, b =2
So, ab = 0*2= 0
a + b = 0 + 2 = 2
Then, (0,2)∈f
But a/c to condition of function it's not possible .(see the daigram).[ 1st set contains more then one image in another set ]
Hence, it's not a function.