Question

Q.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.

No spam​

Answer 1

$\huge\bold{\underline{\underline{{Answer:}}}}$

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.