Discrete mathematics

It's about Discrete mathematics in this book #Anthony Croft, Engineering Mathematices, 5e (2017)

So i will choose exercise 5.2 #7 #8 #9 to slow everyone:

7. The sets A, B and C are given by A = {1, 3, 5, 7, 9},
B = {0, 2, 4, 6} and C = {1, 5, 9} and the universal

set, E = {0,1, 2, . . . ,9}.
(a) Represent the sets on a Venn diagram.
(b) State A ∪ B.
(c) State B ∩ C.
(d) State E ∩ C.
(e) State not A.
(f) State not B ∩not C.
(g) State not (B ∪C).

Ans :

a) Represent the sets on a Venn diagram :

The set containing all the numbers of interest is called the
universal set, E. E is represented by the rectangular region. Sets A , B and C are represented by the interiors of the circles and it is evident that 1, 3, 5, 7 and 9 are members of A while 0,
2, 4, and 6 are members of B that 1, 5 and 9 are members of C. The elements 1 , 5 and 9 are common to both sets.

b) State A ∪ B :

The set which contains all the elements of A and those of B is

called the union of A and B, written as

b) {0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 9}

c) State B ∩ C :

the set B ∩ C has no elements we say the sets B and C are disjoint and write B ∩ C = empty set.

d) State E ∩ C :

The set which contains the elements common to both E and C is called the intersection of E and C, written as

d) {1 , 5 , 9}

e) State not A :

The set of members of E that are not in A is called the complement of A :

e) {0 , 2 , 4 , 6 , 8}

f) State not B ∩ not C :

The set of members of E that are not in B and not in C is called the complement of B and C :

f) {3 , 7 , 8}

g) State not (B ∪C) :

The set which contains all the elements of not A and those of not B is called the union of not A and not B, written as

g) {3 , 7 . 8}

8.Use Venn diagrams to illustrate the following for
general sets C and D:

(a) C ∩D (b) C ∪ D (c) C ∩ not_D
(d) not (C ∪D) (e) not (C ∩D)

Ans :

a) C ∩D :

The set which contains the elements common to both C and D is called the intersection of C and D, written as

b) C ∪ D :

The set which contains all the elements of C and those of D is

called the union of C and D, written as

c) C ∩ not_D :

The set which contains the elements common to both C and D is called the intersection of C and D, written as

d) not (C ∪D) :

e) not (C ∩D) :

9.By drawing Venn diagrams verify De Morgan’s laws

A1 . not(A ∩B) =notA ∪ notB

The set which contains all the elements of A and those of B is called the union of A and B, but Not (A and B)
the set which not contains all the elements of A and those of B.