Math, asked by salini800263, 9 months ago

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.​

Answers

Answered by ITZINNOVATIVEGIRL588
11

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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.

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➡️Given relation f is defined as

➡️f = {(ab, a + b): a, b ∈ Z}

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

➡️As 2, 6, –2, –6 ∈ Z, (2 × 6, 2 + 6), (–2 × –6, –2 + (–6)) ∈ f

➡️i.e., (12, 8), (12, –8) ∈ f

➡️It’s clearly seen that, the same first element, 12 corresponds to two different images (8 and –8).

➡️Therefore, the relation f is not a function.

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Answered by Anonymous
4

Answer:

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.

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