# NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems

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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