# NCERT Class 11-Math՚s Exemplar Chapter 1 Sets CBSE Board Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 11**:

Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.

**Answer**:

**Question 12**:

For all sets A, B and C, show that

Determine whether each of the statement in Exercises is true or false. Justify your answer.

**Answer**:

Given: There are three sets A, B and C

To prove:

Let

Let y

and

and

We know:

and

From (i) and (ii) :

**Question 13**:

For all sets A and B,

**Answer**:

True

**Question 14**:

For all sets A, B and C,

**Answer**:

False

**Question 15**:

For all sets A, B and C, if A ⊂ B, then

**Answer**:

True

**Question 16**:

For all sets A, B and C, if A ⊂ B, then

**Answer**:

True

**Question 17**:

For all sets A, B and C, if and , then .

**Answer**:

True

Using properties of sets prove the statements given in Exercises 18 to 22

**Question 18**:

For all sets A and B,

**Answer**:

Given: There are two sets A and B

To prove:

Take L. H. S

Distributive property of set:

= R. H. S

Hence Proved