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 function from $A$ to $B$? Justify your answer.
(B) relation $f$ from a set $A$ to a set $B$ is a function if every element of $A$ has one and only one image in $B$.
Given $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$.
Here,the element $2 \in A$ is associated with two different images in $B$,which are $9$ and $11$ (i.e.,$f(2) = 9$ and $f(2) = 11$).
Since an element of the domain cannot have more than one image in the codomain,$f$ is not a function.
Given $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$.
Here,the element $2 \in A$ is associated with two different images in $B$,which are $9$ and $11$ (i.e.,$f(2) = 9$ and $f(2) = 11$).
Since an element of the domain cannot have more than one image in the codomain,$f$ is not a function.
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Similar Questions
Let $A = \{a, b, c, d\}$ and $B = \{1, 2, 3\}$. The relations $R_1, R_2, R_3, R_4$ are defined as follows:
$R_1 = \{(a, 1), (b, 2), (c, 1), (d, 2)\}$
$R_2 = \{(a, 1), (b, 1), (c, 1), (d, 1)\}$
$R_3 = \{(a, 2), (b, 3), (c, 2), (d, 2)\}$
$R_4 = \{(a, 1), (b, 2), (a, 2), (d, 3)\}$
Which of the following is true?
$R_1 = \{(a, 1), (b, 2), (c, 1), (d, 2)\}$
$R_2 = \{(a, 1), (b, 1), (c, 1), (d, 1)\}$
$R_3 = \{(a, 2), (b, 3), (c, 2), (d, 2)\}$
$R_4 = \{(a, 1), (b, 2), (a, 2), (d, 3)\}$
Which of the following is true?
Which of the following is $NOT$ a function?
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View SolutionWhich of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
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$\{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}$
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