Question

Given that

$\sf U = \{1,2,3,4,5,6,7,8 \}$

$\sf A = \{1,2,3,5 \}}$

$\sf B = \{2,3,5,6\}$

$\sf C = \{1,7,8\}$

find the value of :-

$\bigstar \sf (AnB)-C$
Have a great answering time :D

#BeBrainly :)​

Answer 1

Given :-

U = { 1,2,3,4,5,6,7,8 }

A = { 1,2,3,5 }

B = { 2,3,5,6 }

C = { 1,7,8 }

To Find :-

The set of ( A ∩ B ) - C

Used Concepts :-

For sets , A and B :-

• ( A ∩ B ) is the set consisting all the common elements of A and B .
• ( A - B ) is the set of elements which belongs to A but not to B .

Solution :-

As Here , The Universal Set ( U ) is given , So in this question all elements of any set is taken from the Universal Set ( U ) .

First , we will Find , ( A ∩ B )

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

B = { 2 , 3 , 5 , 6 }

C = { 1 , 7 , 8 }

Now ,

A ∩ B = { 2 , 3 , 5 }

Now , ( A ∩ B ) - C

{ 2 , 3 , 5 } - { 1 , 7 , 8 }

Here , There is no element present in C which is a member of ( A ∩ B ) .

So , ( A ∩ B ) - C = A ∩ B = { 2 , 3 , 5 } .

For The Euler - Venn diagram kindly see the attachment.

Additional Information :-

For any set "A" :-

• The power set of "A" is the set of all subsets of "A" .
• If n( A ) = m , then no. of subsets of "A" is 2^m .
• If n(A) = m ,then no. of proper subsets of "A" is 2^m -1 .
• Every set is a subset of itself but not proper subset .
• The empty / void / null set is the subset of every set ( Including Itself ) .
• The empty set is proper subset of every set ( Except Itself ) .
• Let , another set "B" then "A" is called the proper subset of "B" if and only all elements of A is also a member of B but there is at least one member in B that is not a member of A .
• n(A) can also be written as O(A) and is the cardinal number / Order of set A .
• Cardinal number is the no. of elements present in a given set .

Thank You !

Answer 2

A n B = {2, 3, 5}

(A n B) - C = (A n B ) - ( A n B n C)

= {2, 3, 5} - { ¢ }

= {2, 3, 5}