#### Question

# Set operations...and the laws of set theory?

Let A,B,C,D,E be a subset of (integer) Z be defined as:

A = {2n I n E Z} -----> that is A is the set of all (integer) multiples of 2;

B = {3n I n E Z};

C = {4n I n E Z};

D = {6n I n E Z}; and

E = {8n I n E Z};

a) which of the following statements are true and which are false?

i) E is a subset of C and C is a subset of A

ii) A is a subset of C and C is a subset of E

iii) B is a subset of D

iv) D is a subset of B

v) D is a subset of A

vi) the complement of set D is a subset of the complement of set A

b) Determine each of the following sets:

i) C and E

ii) B U D

iii) A and B

iv) B and D

v) the complement of set A

vi) A and E

WHAT DOES IT MEAN TO DETERMINE THESE?

#### Answer

) E is a subset of C and C is a subset of A is TRUE.

ii) A is a subset of C and C is a subset of E is FALSE.

iii) B is a subset of D is FALSE.

iv) D is a subset of B is TRUE.

v) D is a subset of A is TRUE.

vi) the complement of set D is a subset of the complement of set A is FALSE.

b) Determine each of the following sets: I assume and means intersection here.

i) C and E = C

ii) B U D = B

iii) A and B includes all multiples of 2 and all multiples of 3.

iv) B and D = D

v) the complement of set A is all odd numbers (positive and negative).

vi) A and E = E.