Class 11 Maths Chapter 2 Relations and Functions – Exercise 2.1 NCERT Solutions

Introduction

Exercise 2.1 introduces the concept of relations between two sets. A relation is a subset of the Cartesian product of two sets. You will learn how to form ordered pairs, define relations, and represent them using arrow diagrams, tables, and set notation.

Formula / Key Concepts

1. Cartesian Product: For sets $A$ and $B$:

$$A\times B=\{(a,b):a\in A,b\in B\}$$

2. Relation: A relation $R$ from set $A$ to set $B$ is a subset of $A\times B$.

3. Domain of Relation: Set of all first elements of ordered pairs in $R$.

4. Range of Relation: Set of all second elements of ordered pairs in $R$.

5. Codomain: The set $B$ in relation $R\subseteq A\times B$.

NCERT Questions with Solutions (10)

Q1. If $A=\{1,2\},B=\{3,4\}$, find $A\times B$.

$$A\times B=\{(1,3),(1,4),(2,3),(2,4)\}$$

Q2. If $A=\{a,b\},B=\{1,2,3\}$, find $A\times B$.

$$A\times B=\{(a,1),(a,2),(a,3),(b,1),(b,2),(b,3)\}$$

Q3. If $A=\{1,2\},B=\{x,y\}$, find $B\times A$.

$$B\times A=\{(x,1),(x,2),(y,1),(y,2)\}$$

Q4. If $A=\{1,2,3\},B=\{4,5\}$, find number of elements in $A\times B$.

$$n(A\times B)=n(A)\cdot n(B)=3\cdot 2=6$$

Q5. If $A=\{1,2\},B=\{3,4,5\}$, find number of elements in $B\times A$.

$$n(B\times A)=3\cdot 2=6$$

Q6. If $A=\{1,2\},B=\{3\}$, find $A\times B$.

$$A\times B=\{(1,3),(2,3)\}$$

Q7. If $A=\{a,b,c\},B=\{1,2\}$, find $A\times B$.

$$A\times B=\{(a,1),(a,2),(b,1),(b,2),(c,1),(c,2)\}$$

Q8. If $A=\{1,2\},B=\{x,y,z\}$, find $A\times B$.

$$A\times B=\{(1,x),(1,y),(1,z),(2,x),(2,y),(2,z)\}$$

Q9. If $A=\{1\},B=\{2,3,4\}$, find $A\times B$.

$$A\times B=\{(1,2),(1,3),(1,4)\}$$

Q10. If $A=\{p,q\},B=\{1,2\}$, find $A\times B$.

$$A\times B=\{(p,1),(p,2),(q,1),(q,2)\}$$

FAQs (10)

1. What is Cartesian product? Set of all ordered pairs from two sets.

2. What is relation? Subset of Cartesian product.

3. What is domain? Set of first elements of ordered pairs.

4. What is range? Set of second elements of ordered pairs.

5. What is codomain? The second set in relation definition.

6. Can relation be empty? Yes, if no ordered pairs satisfy condition.

7. Can relation be universal? Yes, if relation = entire Cartesian product.

8. What is arrow diagram? Graphical representation of relation.

9. What is ordered pair? Pair $(a,b)$ with order significant.

10. Why is this exercise important? It builds foundation for functions and mappings.

Conclusion

Exercise 2.1 has 10 solved questions and 10 FAQs that strengthen your understanding of relations and Cartesian products. This builds the foundation for advanced topics in Class 11 Maths.

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