Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$,and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a relation from $A$ to $B$? Justify your answer.
(A) relation from a set $A$ to a set $B$ is defined as a subset of the Cartesian product $A \times B$.
Given $A = \{1, 2, 3, 4\}$ and $B = \{1, 5, 9, 11, 15, 16\}$.
The Cartesian product $A \times B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.
Since every element in the set $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$ satisfies the condition that the first component belongs to $A$ and the second component belongs to $B$,we can conclude that $f \subseteq A \times B$.
Therefore,$f$ is a relation from $A$ to $B$.
Given $A = \{1, 2, 3, 4\}$ and $B = \{1, 5, 9, 11, 15, 16\}$.
The Cartesian product $A \times B$ consists of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.
Since every element in the set $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$ satisfies the condition that the first component belongs to $A$ and the second component belongs to $B$,we can conclude that $f \subseteq A \times B$.
Therefore,$f$ is a relation from $A$ to $B$.
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