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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.
(i) $f$ is a relation from $A$ to $B$
(ii) $f$ is a function from $A$ to $B$
Justify your answer in each case.
Solution:
1745 Upvotes
Verified Answer
(i) $f$ is a subset of $A \times B$.
$\therefore f$ is a relation from $A$ to $B$.
(ii) The element $2 \in A$, has two images 9 and 11 .
$\therefore f$ is not a function from $A$ to $B$.
$\therefore f$ is a relation from $A$ to $B$.
(ii) The element $2 \in A$, has two images 9 and 11 .
$\therefore f$ is not a function from $A$ to $B$.
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