Question

3. 03. If A and B are two sets, then A- (A-B)is equal to
a) B b)AuB. c)AnB. d)B-A
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Answer 1

Answer: If A and B are two sets, then A- (A-B)is equal to A∩B. Do the problem using Venn diagram.

Step-by-step explanation:

Answer 2

Answer:

A-(A-B) would be equal to A ∩ B i.e option (c) is correct

Step-by-step explanation:

• A and B are 2 sets given to us
• A-B means the set of all elements which present in A but not in B

        e.g A= {1,2,3,4} and B = {2,3,4,5}

        So A-B will all {1}  and B-A would be {5}

• We are asked to find A - ( A - B )

Step 1:

• First let us solve bracket
• Assume A= {1,2,3,4} and B = {2,3,4,5} for proper understanding
• A - B will be all those elements of A which are not in B and here 1 is the only element which is present in A not in B
• Therefore C=A-B ={ 1 }

Step 2:

• Now find A-C where C = { 1 }
• A - C = { 1,2,3,4} - { 1 }

       We get A - C = { 2, 3 , 4} which same as the intersection of A and B

       i.e. A ∩ B = { 2,3,4}

Therefore A - ( A - B ) will be equal to A ∩ B