Question

Question 10 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.

Class X1 - Maths -Relations and Functions Page 46

Answer 1

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.