Question

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

Answer 1

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

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 A.

e.g., A' = U - A = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4}
= {5, 6, 7, 8, 9}

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

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

Answer 2

A cap A' = { }

Explanation:

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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' ):

A' = U - A

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

A = { 2,3,5,7 }

i ) A' = U - A

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

= { 1,4, 6 }

ii ) A cap A'

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

= { }

= empty Set

Therefore ,

A cap A' = { }

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