Question

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
(i) f is a relation from A to B (ii) f is a function from A to B.
Justify your answer in each case.
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Answer 1

Answer:

Here,

A = {1,2,3,4}

B={1,5,9,11,15,16}

f={(1,5),(2,9),(3,1),(4,5),(2,11)}

(i) f⊂AxB{ f is subset of AxB}

Hence, it is a relation from A to B.

(ii)according to definition of function we know that function is a realtion from one set to another set when every element of 1st set has one and only one image in another set.

Here, we see that the odered pair (2,9) and (2,11) have the same 1st components.

Hence, it's not a function.

Answer 2

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$\Large\fbox{\color{purple}{QUESTION}}$

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.

Are the following true?

(i) f is a relation from A to B (ii) f is a function from A to B.

Justify your answer in each case.

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➡️Given,

➡️A = {1, 2, 3, 4} and B = {1, 5, 9, 11, 15, 16}

➡️So,

➡️A × B = {(1, 1), (1, 5), (1, 9), (1, 11), (1, 15), (1, 16), (2, 1), (2, 5), (2, 9), (2, 11), (2, 15), (2, 16), (3, 1), (3, 5), (3, 9), (3, 11), (3, 15), (3, 16), (4, 1), (4, 5), (4, 9), (4, 11), (4, 15), (4, 16)}

➡️Also given that,

➡️f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

✴(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B.

➡️It’s clearly seen that f is a subset of A × B.

➡️Therefore, f is a relation from A to B.

✴(ii) As the same first element i.e., 2 corresponds to two different images (9 and 11), relation f is not a function.

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