Question

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

Answer 1

answer : $\boxed{\bf{U'\cap A=\emptyset}}$

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 universal set , U.
we know, complement of set R is the set of all distinct elements in U but not in R.
U' = U - U = $\emptyset$

now, $U'\cap A$ = $\emptyset \cap${1, 2, 3, 4}
= $\emptyset$

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

Answer 2

U' ∩ 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

Intersection of sets :

Let A and B be two sets . Then

the intersection of A and B , is

the set of all those elements which

are common to both A  and B.

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

A = { 2,3,5,7 }

i ) U' = U - U

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

= ∅

ii ) U' ∩ A

= { } ∩ { 2,3,5,7 }

= ∅

= empty Set.

Therefore ,

U' ∩ A = ∅

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