Question

Let A= {2,4,6,8}&B{6,8,10,12} 1) write AUB&Anb 2) wrie A-B& B-A 3) write number of subsets of AUB​

Answer 1

Step-by-step explanation:

Given :-

A= {2,4,6,8}

B = {6,8,10,12}

To find :-

Find the following :

1) AUB

2) AnB

3) A-B

4) B-A

5) Number of Subsets of AUB

Solution :-

Given sets are :

A= {2,4,6,8}

B = {6,8,10,12}

I) AUB:-

=>{ 2,4,6,8 } U { 6,8,10,12 }

=> { 2,4,6,8,10,12 }

AUB = { 2,4,6,8,10,12 }

ii) AnB:-

=>{ 2,4,6,8 } n { 6,8,10,12 }

=> { 6,8 }

AnB = { 6,8 }

iii) A-B:-

=>{ 2,4,6,8 } - { 6,8,10,12 }

=> { 2,4}

A-B = { 2,4 }

iv) B-A:-

=> { 6,8,10,12 } - { 2,4,6,8 }

=> {10,12 }

B-A = { 10,12 }

v) Number of Subsets of AUB :-

AUB = {2,4,6,8,10,12 }

Number of elements in the set AUB = 6

We know that

If the number of elements in the set A is 'n' then the number of sub sets to A = 2^n

We have n = 6

Total number of subsets to AUB = 2⁶

=> 2×2×2×2×2×2

=> 64

Number of Subsets of AUB = 64

Answer:-

1)AUB = { 2,4,6,8,10,12 }

2)AnB = { 6,8 }

3)A-B = { 2,4 }

4)B-A = { 10,12 }

5)Number of Subsets of AUB = 64

Used formulae:-

• AUB is the set of the all elements in either A or in B or in both.
• AUB = {x:x€A or x€B}
• AnB is the set of all common elements in both sets A and B.
• AnB={x:x€A and x€B}
• A-B is the set of all elements in only the set A
• A-B ={x:x€A and x doesn't € B}
• B-A is the set of all elements in only the set B
• B-A ={x:x€B and x doesn't € A}
• If the number of elements in the set A is 'n' then the number of sub sets to A = 2^n