# NCERT Class 11 Mathematics Solutions: Chapter 1 –Sets Miscellaneous Exercise Part 5

1. Show that need not imply .

Consider,

Accordingly,

Here,

However,

2. Let be sets. If for some set,

show that .

(Hints and use distributive law)

Consider be two sets such that for

some set to show .

It can be seen that

[Distributive law]

……………….. eq (1)

Now,

[Distributive law]

……………………… eq (2)

Hence, from (1) and (2), we obtain .

2. Find sets A, B and C such that are non-empty sets and .

Consider .

Accordingly,

are non-empty.

However,

3. In a survey of students in a school, students were found to be taking tea and taking coffee, were taking both tea and coffee. Find how many students were taking neither tea nor coffee.

Consider be the set of all students who took part in the survey.

Consider be the set of students taking tea.

Consider be the set of students taking coffee.

Accordingly,

To find: Number of student taking neither tea nor coffee i.e.,

We have to find .

Hence, students were taking neither tea nor coffee.