Question

Fill in the blank to make the given statement true : $\phi' \cap A$ =_____

Answer 1

answer : $\emptyset'\cap A=A$

for understanding, Let us assume that A = {1, 2, 3, 4} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

first find complement of empty set.
$\emptyset'=U-\emptyset=U$

e.g., $\emptyset'$ = {1, 2, 3, 4, 5, 6, 7, 8, 9}

now, $\emptyset'\cap A=U\cap A$

= {1, 2, 3, 4, 5, 6 , 7, 8, 9} $\cap$ {1, 2, 3, 4}

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

hence, $\bf{\emptyset'\cap A=A}$

Answer 2

{ }' cap A = A

Explanation :

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Empty Set :{ }

A set with no elements in it is

called an Empty Set.

Universal set ( U ):

A set which consists of all the sets

under consideration or discussion

is called the universal set.

Complement of set A :( A' )

Complement of set A is denoted by A'

A' = U - A

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

A = { 2,3,5,7 }

i ) { } ' = U - { }

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

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

= U

ii ) { }' cap A = U cap A

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

= { 2,3,5,7 }

= A

Therefore ,

{ }' cap A = A

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