True/False: 1) The following sets are identical: and {} 2) The following sets ar

Question

True/False:

1) The following sets are identical:

and {}

2) The following sets are identical:

and { x | x is an odd number divisible by 2 }

3) The following sets are identical:

{ 1, 3, 2 } and { 3, 2, 1, 1, 2 }

4) The following sets are identical:

{1} and {1, {1} }.

5) The following sets are identical:

B - A and A - B

where A and B are different sets.

6) The following sets are identical:

B A and A B.

7) The following sets are identical:

B   A and A B.

8) The following sets are identical:

A ( B C ) and ( A B ) C.

Explanation / Answer

1. False

    represents empty set i.e. {} and {} represents non empty set that contains . Therefore and {} are not identical.

2. True

{ x | x is an odd number divisible by 2 } is empty set { } i.e. . Therefore they are identical.

3. True

We can right same elements only once in a set. Therefore { 1, 3, 2 } = { 3, 2, 1, 1, 2 } and identical.

4. False

{1} and {1, {1} } are not identical because second set contains element 1 and also has set {1).

5. False

A-B is set of elements that present in A but not in B and B-A is a set of elememts that present in B but not in A, Therefore A-B and B-A are not identical.

6. True

    Subset operation in set satisfies commutative property i.e. B A = A B. Therefore B A and A B are identical.

7. True

Union operation in set satisfies commutative property i.e. B A = A B. Therefore B A and A B are identical.

8. True

Union operation in set satisfies Associative property i.e. A ( B C ) = ( A B ) C. Therefore A ( B C ) and ( A B ) C are identical.

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