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  • Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b belongs to Z}. Is f a function from Z to Z? Justify your answer.

Q11  Let f be the subset of Z \times Z defined by f = {(ab, a + b) : a, b \epsilon Z} . Is f a
         function from Z to Z? Justify your answer.

Answers (1)

best_answer

It is given that 
f = {(ab, a + b) : a, b \epsilon Z}
Now, we know that relation f from a set A to a set B is said to be a function only if every element of set A has a unique image in set B 
Now,  for value 2, 6, -2, -6 \epsilon \ Z
f = \left \{ (2 ×\times 6, 2 + 6), (-2 \times -6, -2 - 6), (2 \times -6, 2 - 6), (-2 \times 6, -2 + 6) \right \}
\Rightarrow f = \left \{ (12, 8), (12, -8), (-12, -4), (-12, 4) \right \}
Now,  we can observe that same first element i.e. 12 corresponds to two different images that are 8 and -8.
Thus, f   is not a function

Posted by

Gautam harsolia

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