Set Theory Problems and Solutions

Introduction to set theory problems and solutions:
A set theory should be one of the major concepts in mathematics. All the operations in set theory could be based on sets. Set should be a group of individual terms in domain. The universal set is set that having every element of domain. Finding the solutions for set theory problems are very easy. Here we will see about the example problems with solutions in set theory.

Example Problems:

Let we see few set theory problems and solutions.

Example 1:

If the sets, P, Q and R are, P = {1,2,3,4,5,6}, Q = {2,5,7,9} and R = {2,4,7,10}. Find,

i) P?(QnR)

ii) Pn(QnR)

Solution:

Given, sets P, Q and R are,

P = {1,2,3,4,5,6}

Q = {2,5,7,9}

R = {2,4,7,10}

i) P?(QnR):

First we need to find QnR.

QnR = {2,7}

Then, P?(QnR) = {1,2,3,4,5,6} ? {2,7}

= {1,2,3,4,5,6,7}

ii) Pn(QnR):

First we need to find QnR.

QnR = {2,7}

Now, Pn(QnR) = {1,2,3,4,5,6} n {2,7}

= {2}

Example 2:

Prove the associative laws for the sets A = {a,b,c,d,e,f}, B = {a,c,g,h} and C = {b,c,g,h,k}.

Solution:

Given sets are,

A = {a,b,c,d,e,f}

B = {a,c,g,h}

C = {b,c,g,h,k}

Associative laws are,

i) A?(B?C) = (A?B)?C

ii) An(BnC) = (AnB)nC

i) A?(B?C) = (A?B)?C:

Find A?(B?C):

B?C = {a,b,c,g,h,k}

A?(B?C) = {a,b,c,d,e,f,g,h,k}

Find (A?B)?C:

A?B = {a,b,c,d,e,f,g,h}

(A?B)?C = {a,b,c,d,e,f,g,h,k}

Therefore, A?(B?C) = (A?B)?C.

ii) An(BnC) = (AnB)nC:

Find An(BnC):

BnC = {c,g,h}

An(BnC) = {c}

Find (AnB)nC:

AnB = {a,c}

(AnB)nC = {c}

Thus, An(BnC) = (AnB)nC.

Hence, the associative laws are proved. Please express your views of this topic how to round numbers by commenting on blog.

Example Problem 3:

The sets A = {1,2,3,4}, B = {2,3,5,6} and C = {1,2,6,7,8}. Find,

i) A-B

ii) A-(BnC)

Solution:

Given sets are,

A = {1,2,3,4}

B = {2,3,5,6}

C = {1,2,6,7,8}

Find A-B:

A-B means that the set of numbers that are in A not in B. That is,

A-B = {1,4}

Find A-(BnC):

BnC = {2,6}

A-(BnC) = {1,3,4}

Answer:

i) A-B = {1,4}

ii) A-(BnC) = {1,3,4}

These are few set theory problems with solutions.