Class 11 Maths Chapter 1 Sets – Exercise 1.2 NCERT Solutions

Class 11 Maths Chapter 1 Sets – Exercise 1.2 NCERT Solutions

Introduction

Exercise 1.2 focuses on operations on sets such as union, intersection, difference, and complement. These operations are fundamental in set theory and are widely applied in mathematics, computer science, and logic.

Formula Used

1. Union of sets:

$$A\cup B=\{x:x\in A\text{ or }x\in B\}$$

2. Intersection of sets:

$$A\cap B=\{x:x\in A\text{ and }x\in B\}$$

3. Difference of sets:

$$A-B=\{x:x\in A\text{ and }x\mathrm{\notin }B\}$$

4. Complement of set:

$$A^{\mathrm{\prime }}=\{x:x\in U\text{ and }x\mathrm{\notin }A\}$$

Where $U$ is the universal set.

NCERT Questions with Solutions (10)

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

$$A\cup B=\{1,2,3,4\}$$

Q2. If $A=\{1,2,3\},B=\{2,3,4\}$, find $A\cap B$.

$$A\cap B=\{2,3\}$$

Q3. If $A=\{1,2,3\},B=\{2,3,4\}$, find $A-B$.

$$A-B=\{1\}$$

Q4. If $A=\{1,2,3\},B=\{2,3,4\}$, find $B-A$.

$$B-A=\{4\}$$

Q5. If $U=\{1,2,3,4,5\},A=\{1,2,3\}$, find $A^{\mathrm{\prime }}$.

$$A^{\mathrm{\prime }}=\{4,5\}$$

Q6. If $U=\{a,b,c,d,e\},A=\{a,c,e\},B=\{b,c,d\}$, find $A\cup B$.

$$A\cup B=\{a,b,c,d,e\}$$

Q7. If $U=\{a,b,c,d,e\},A=\{a,c,e\},B=\{b,c,d\}$, find $A\cap B$.

$$A\cap B=\{c\}$$

Q8. If $U=\{1,2,3,4,5,6\},A=\{1,2,3\},B=\{3,4,5\}$, find $A\cup B$.

$$A\cup B=\{1,2,3,4,5\}$$

Q9. If $U=\{1,2,3,4,5,6\},A=\{1,2,3\},B=\{3,4,5\}$, find $A\cap B$.

$$A\cap B=\{3\}$$

Q10. If $U=\{1,2,3,4,5,6\},A=\{1,2,3\},B=\{3,4,5\}$, find $A^{\mathrm{\prime }},B^{\mathrm{\prime }}$.

$$A^{\mathrm{\prime }}=\{4,5,6\},B^{\mathrm{\prime }}=\{1,2,6\}$$

FAQs (10)

1. What is union of sets? Combination of elements from both sets.

2. What is intersection of sets? Common elements of both sets.

3. What is difference of sets? Elements of one set not in the other.

4. What is complement of set? Elements of universal set not in given set.

5. What is universal set? Set containing all elements under consideration.

6. Can union be empty? No, unless both sets are empty.

7. Can intersection be empty? Yes, if sets have no common elements.

8. What is disjoint set? Sets with empty intersection.

9. What is cardinality of union? $\mathrm{\mid }A\cup B\mathrm{\mid }=\mathrm{\mid }A\mathrm{\mid }+\mathrm{\mid }B\mathrm{\mid }-\mathrm{\mid }A\cap B\mathrm{\mid }$.

10. Why is this exercise important? It builds foundation for advanced set operations and Venn diagrams.

Conclusion

Exercise 1.2 has 10 solved questions and 10 FAQs that strengthen your understanding of set operations. This builds the foundation for advanced topics in Class 11 Maths.

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