WELCOME

Md. Easin Arafat ChowdhuryDept. of Computer Science & EngineeringID No: 162015040Batch No: 1602

Green University of Bangladesh

Slide-01

The Theory of sets was developed by German mathematician Georg Cantor (1845-1918). He first encountered sets while working on “Problems on Trigonometric Series”. SETS are being used in mathematics problem since they were discovered.

Georg Cantor(1845-1918).

Slide-02

(1) Let U = {1,2, …, 9} be the universal set, and let

A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7}

C = {5, 6, 7, 8, 9}

D = {1, 3, 5, 7, 9}

E = {2, 4, 6, 8}

F = {1, 5, 9}

Slide-03

Here,

A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7}, C= {5, 6, 7, 8, 9}, D= {1, 3, 5, 7, 9}

E= {2, 4, 6, 8}, F = {1, 5, 9}.

Find: (a) A B and A∩B (b) A C and A∩C (c) D F and D∩F.∪ ∪ ∪

(a) A B = {1, 2, 3, 4, 5, 6, 7} and A ∩ B = {4, 5}∪ (b) A C = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A ∩ C = {5}∪ (c) D F = {1, 3, 5, 7, 9} = D and D ∩ F = (1, 5, 9)∪

Slide-04

List the elements of each set where N = {1, 2, 3, .…}. (a) A = {x ∈ N| 3 < x < 9}(b) B = {x ∈ N| x is even, x < 11}(c) C = {x ∈ N| 4 + x = 3}

(a) A consists of the positive integers between 3 and 9; hence A = {4, 5, 6, 7, 8}.

(b) B consists of the even positive integers less than 11; hence B = {2, 4, 6, 8, 10}.

(c) No positive integer satisfies 4 + x = 3; hence C = , the empty set.∅

Slide-05