Class 11 Mathematics Relations and Functions Relations

Medium

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

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Solution

(N/A) The given relation is $R = \{(1,3), (1,5), (2,5)\}$.
In a relation,for it to be a function,every element of the domain must have a unique image in the codomain.
Here,the element $1$ in the domain is associated with two different images,$3$ and $5$.
Since the same first element $1$ corresponds to two different images,this relation is not a function.

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Class 11

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Relations and Functions

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Relations

Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

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If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$,then the number of relations from $A$ to $B$ is

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Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R$ implies $(b, a) \in R$

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Let $A = \{2, 3, 4, 5\}$ and $B = \{3, 6, 7, 10\}$. $A$ relation $R$ is defined from $A$ to $B$ such that $xRy \iff x$ is relatively prime to $y$. What is the domain of $R$?

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Define a relation $R$ on the set $N$ of natural numbers by $R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in N\}$. Depict this relationship using roster form. Write down the domain and the range.

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Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.$\{(1,3), (1,5), (2,5)\}$

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Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$,then the number of relations from $A$ to $B$ is

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?$(a, b) \in R$ implies $(b, a) \in R$

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Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R$ implies $(b, a) \in R$