Question

let f be the subset of z×z defined by f={(a, b, a+b):ab€z} is f a function from z to z? justify your answer​

Answer 1

Answer:

The relation f is defined as

f={(ab,a+b):a,b∈Z}

We know that a relation f from set A to set B is said to be a function if every element of set A has unique images in set B.

Since  2,6∈Z,

⇒(2×6,2+6)∈f

Again since, −2,−6∈Z,

⇒(−2×−6,−2+(−6))∈f

i.e., (12,8),(12,−8)∈f 

It can be seen that the same first element i.e., 12 corresponds to two different images i.e., 8 and −8.

 Thus relation f is not a function

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