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Relations and Functions EXERCISE 2.2 Solutions
- Q1: Let $A = \{1, 2, 3,...,14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x – y = 0, \text{where } x, y \in A\}$. Write down its domain, codomain and range.
- Q2: Define a relation $R$ on the set $\mathbb{N}$ of natural numbers by $R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in \mathbb{N}\}$. Depict this relationship using roster form. Write down the domain and the range.
- Q3: $A = \{1, 2, 3, 5\}$ and $B = \{4, 6, 9\}$. Define a relation $R$ from $A$ to $B$ by $R = \{(x, y): \text{the difference between } x \text{ and } y \text{ is odd}; x \in A, y \in B\}$. Write $R$ in roster form.
- Q4(i): The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (i) in set-builder form. What is its domain and range?
- Q4(ii): The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (ii) roster form. What is its domain and range?
- Q5(i): Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (i) Write $R$ in roster form.
- Q5(ii): Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (ii) Find the domain of $R$.
- Q5(iii): Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (iii) Find the range of $R$.
- Q6: Determine the domain and range of the relation $R$ defined by $R = \{(x, x + 5) : x \in \{0, 1, 2, 3, 4, 5\}\}$.
- Q7: Write the relation $R = \{(x, x^3) : x \text{ is a prime number less than } 10\}$ in roster form.
- Q8: Let $A = \{x, y, z\}$ and $B = \{1, 2\}$. Find the number of relations from $A$ to $B$.
- Q9: Let $R$ be the relation on $\mathbb{Z}$ defined by $R = \{(a,b): a, b \in \mathbb{Z}, a – b \text{ is an integer}\}$. Find the domain and range of $R$.
Other Exercises for CBSE - Class 11 Mathematics Relations and Functions
Chapters in CBSE - Class 11 Mathematics
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