NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.5

The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5 solve every question of the fifth exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.

Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.

Exercise 1.5 introduces the complement of a set and De Morgan's laws. The exercise has 7 questions built around these skills:

• Finding the complement A′ of a set inside a universal set U.
• Verifying De Morgan's laws for union and intersection.
• Drawing Venn diagrams for complement expressions.

Topics Covered in Sets Exercise 1.5

This exercise depends on a fixed universal set U. The complement A′ is the set of all elements of U that are not in A. Two key results, called De Morgan's laws, connect complement with union and intersection. Venn diagrams give a clear picture of each result.

• Complement: if U = {1, ..., 9} and A = {1, 2, 3, 4}, then A′ = {5, 6, 7, 8, 9}.
• De Morgan's first law: (A ∪ B)′ = A′ ∩ B′.
• De Morgan's second law: (A ∩ B)′ = A′ ∪ B′.
• Venn diagrams: shading shows A′, (A ∪ B)′ and similar sets.

Important: a complement only makes sense once the universal set U is fixed. The same set A has a different complement under a different U.

Question-wise Breakdown of Sets Exercise 1.5

The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5 answer all 7 questions in order. The table shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.

Questions 4 and 5 carry the most weight, since De Morgan's laws and Venn diagrams appear often in exams.

Key Formulas and Definitions for Sets Exercise 1.5

Exercise 1.5 rests on the complement and its properties. Students should learn each result before attempting the questions.

Tip: under De Morgan's laws, the complement flips union to intersection and intersection to union. Remembering this one swap solves Question 4 quickly.

Common Mistakes in Sets Exercise 1.5

Students lose easy marks in Exercise 1.5 by forgetting the universal set or misusing De Morgan's laws. The list below covers the errors that show up most often on the NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5.

• Finding a complement without noting U. Always list the universal set first.
• Keeping union as union under a complement. De Morgan's law flips it to intersection.
• Writing A ∩ A′ as U. It is actually the empty set, since nothing is both in and out of A.
• Shading the wrong region in a Venn diagram. Shade only the part that matches the expression.

Practice Questions for Sets Exercise 1.5

After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 1.5.

Other Exercises of Chapter 1 Sets

Chapter 1 Sets has five exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 1.5 is done.

More Class 11 Maths Sets Resources

Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 1 Sets are linked below.

NCERT Solutions for Other Class 11 Maths Chapters

Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.

FAQs on NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.5