Definition of Complement

Introduction to definition of complement:

The complement of set A, indicated by A’, is the set of every elements in the universal set that are not in A. The numeral of elements of A and the numeral of elements of A’ makes up the whole number of elements in U. Let us see about the topic definition of complement are given below examples. Having problem with Binomial Expansion Calculator keep reading my upcoming posts, i will try to help you

Example Problems for Definition of Complement Set

Let us see about the topic definition of complement set are given some example problems with solution are shown in below,

Example problem 1:- Using definition of complement

Let U = {x: x is an integer, –6 = x = 7}, P = {–4, –2, 1, 4, 3, 6, 7} and

Q’ = {–3, –2, –1, 2, 3}. List the elements of set P ’

Solution:

Given:

List the elements of set P ’

First, list out the members of U.

U = {-6,-5,–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6,7}

P’ = {–5,-3,–1, 2, 5, 6} ? in U but not in P

Example problem 2:- Using definition of complement

Let U = {x: x is an integer, –6 = x = 7}, P = {–4, –2, 1, 4, 3, 6, 7} and

Q’ = {–3, –2, –1, 2, 3}. Find n (Q)

Solution:

Given:

Step 1: to calculate n (Q)

U = {-6,-5,–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6,7} and P’ = {–5,-3,–1, 2, 5, 6}

n ( U ) = 14, n(Q ’ ) = 6

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Example Problem 3:- Using Definition of Complement

Let U = {x: x is an integer, –6 = x = 7}, P = {–4, –2, 1, 4, 3, 6, 7} and

Q’ = {–3, –2, –1, 2, 3}. Find n (Q)

Solution:

Given:

Step 1: to calculate n (Q)

U = {-6,-5,–4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6,7} and P’ = {–5,-3,–1, 2, 5, 6}

n ( U ) = 14, n(Q ’ ) = 6

Use the method:

n (Q) + n (Q’ ) = n ( U )

n (Q) = n (U) – n (Q ’ ) = 14 – 6 = 8

Example problem 4:- Using definition of complement

U = set of positive integers less than 7 x = {7, 4, 2, 6, 1} and y = (1, 2, 3, 5}

Find the (X n Y) ‘

Solution:

Given:

Step: 1 we can determine the values of the (X n Y) ‘= {7, 4, 6, 5}

Step: 2 Another method we can calculate (X n Y) = {1, 2}

Step: 3 (X n Y) ‘= {7, 4, 6, 5}