### Sets Quiz #1

*Question 1*

Describe the shaded region (lined region) in each Venn diagram below, using set notation only.

Example:

**Solutions:**

(a) (A U B)’

This notation means, the compliment of A U B. In this case, compliment (‘) means everything outside of the sets A and B.

(b) A ∩ B

This notation means, A intersect B. That is the section that is common to both A and B.

*Question 2 *

(a) Use the Venn diagram above to determine how many elements are in each of the following sets.

(i) (A ∩ B)’ (ii) (A U B)’

(b) Determine which set notation is the same as:

(i) (A ∩ B)’ (ii) (A U B)’

**Solutions:**

(a) (i) (A ∩ B)’ = 18 + 16 + 24

= 58

(ii) (A U B)’ = 24

(b) (i) A’ U B’

Which is the same as (A ∩ B)’.

(ii) A’ ∩ B’

A’ ∩ B’ above, is the same as (A U B)’.

*Questions 3*

A water park has 300 visitors on a certain day. Of that 300,

70 went on the ‘Jamaica Bobsled’ slide only

2x went on the ‘Lightning Bolt’ slide only

80 went on neither slide

x went on both slides

(i) Create a Venn diagram to illustrate the information.

(ii) Calculate the number of visitors who went on the ‘Lightning Bolt’ slide only.

**Solutions:**

(i)

(ii)

*Question 4*

A survey is conducted with 39 students, as to what activities they part-take in over the Christmas Holidays. It was found that:

15 had Family dinners

18 went to parties

x did both

3x did neither

(i) Calculate the value of x.

**Solution:**