1.    
Given that

A =
{1, 2, 6, 9, 10}

B =
{2, 4, 6, 8)

C =
{1, 3, 5, 9}

D =
{ }

E =
{0, 1, 2, 8, 9, 10}

U =
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

 

Find:

a)   
(A’ Ç B’)
Ç (C’
È
D’)’

Solution

 

 

 

 

 

 

 

 

 

 

b)   
(C’ Ç
D’)’ D (A È E’)’

Solution

 

 

 

 

 

 

 

 

 

 

 

c)    
(B’ È D)
– (A Ç E’)

Solution

 

 

 

 

 

 

 

 

 

 

 

 

d)   
(A’ - B’) È (C’
- D’)’

Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

e)   
[(C’ Ç
D’)’ - (A D
E’)’]’

Solution

 

 

 

 

 

 

 

 

 

 

 

2.     In a
chemistry class with 53 students,

20
students used chemical A

19
students used chemical B

31
students used chemical C

12
students used both chemicals A and B

11
students used both chemicals B and C

10
Students used both chemicals A and C

7
students used all the three chemicals A, B, C

 

a)   
How many students used both chemicals A and
B, but not C?

b)   
How many students used both chemicals B and C?

c)    
How many students used at least 2 chemicals?

d)   
How many students used only 1 chemical?

e)   
How many students did not use any of the
chemicals?