Question

(i) $f$ is a relation from $A$ to $B$

(ii) $f$ is a function from $A$ to $B$

Justify your answer in each case

Open in App

Verified by Toppr

$∴A×B={(1,1),(1,5),(1,9),(1,11),(1,15),(1,16),(2,1),(2,5),(2,9),(2,11),(2,15),(2,16),$

$(3,1),(3,5),(3,9),(3,11),(3,15),(3,16),(4,1),(4,5),(4,9),(4,11),(4,15),(4,16)}$

It is 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 is observed that f is a subset of $A×B$

Thus $f$ is a relation from $AtoB$.

(ii) Since the element $2$ corresponds to two different images i.e., $9$ and $11$. So, relation $f$ is not a function

Solve any question of Relations and Functions with:-

0

0