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.

Answer 1

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

$\therefore A\times B=\left\{\right(1,1),(1,5),(1,9),(1,11),$

$(1,15),(1,16),(2,1),(2,5),$

$(2,9),(2,11),(2,15),(2,16),$

$(3,1),(3,5),(3,9),(3,11),$

$(3,15),(3,16),(4,1),(4,5),$

$(4,9),(4,11),(4,15),(4,16),$

$f=\left\{\right(1,5),(2,9),(3,1),(4,5),(2,11\left)\right\}$

Now $(1,5),(2,9),(3,1),(4,5),(2,11)ϵA\times B$

$\therefore$ f is a relation from A to B.

(ii) Here f(2) = 9 and f(2) = 11

$\therefore$ f is not a function from A to B.