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If A,B and C are three sets such that

A\cap B= A\cap C \: and \: A\cup B= A\cup C then

  • Option 1)

    A=C

  • Option 2)

    B=C

  • Option 3)

    A\cap B= \phi

  • Option 4)

    A= B

 

Answers (2)

best_answer

As we learnt in

UNION OF SETS -

Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union.

- wherein

Symbolically, we write A U B = {x: x ∈ A or x ∈ B}.

 

 

INTERSECTION OF SETS -

The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩ ‘is used to denote the intersection.
 

- wherein

Symbolically, we write A ∩ B = {x: x ∈ A and x ∈ B}.

 

 A\cap B=A\cap C  and  A\cup B=A\cup C then B = C

Let x\epsilon A\cap B

    x\epsilon A\ \; and\ \; x\epsion B and y\epsilon A  or  y\epsilon B

So y\epsilon A  and y\epsilon C  and  y\epsilon A  or   y\epsilon B

Both will be equal only and only if B = C

Correct option is 2.

 

 

 


Option 1)

A=C

This is an incorrect option.

Option 2)

B=C

This is the correct option.

Option 3)

A\cap B= \phi

This is an incorrect option.

Option 4)

A= B

This is an incorrect option.

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prateek

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