Question

TRUE OR FALSE. If false, state why the statement is incorrect.
1. all equivalent sets are equal sets.
2. All equal sets are equivalent sets.
3. Sometimes, a subset has higher order than its originating set.
4. A subset can never have an equal number of elements with its originating set.
5. A set with 4 elements has 6 subsets.

Answer 1

Answer:

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Answer 2

Answer:

1) False         2) True          3) False          4) False          5) False

Step-by-step explanation:

1) All equivalent sets are equal sets.

No, equivalent sets are not equal sets.

For example: A = {1, 2, 3} and B = {6, 7, 8}

Clearly, the sets A and B are equivalent but not equal.

Therefore, option (1) is false.

2) All equal sets are equivalent sets.

The equal sets have the exact same elements, hence they must have the same number of elements.

Therefore, equal sets are equivalent sets.

Option (2) is true.

3) A subset has higher order than its originating set.

No, a subset cannot have higher order that its originating set.

For example: If A⊆B, then |A| ≤ |B|, i.e., order of A is less than the order of B.

Therefore, option (3) is false.

4)

It is possible that a subset can have equal number of elements as that of originating set if the subset is the originating set itself.

Therefore, option (4) is false.

5) A set with $4$ elements has $6$ subsets.

The $number$ of subsets are,

= $2^n$, where n = no. of elements.

= $2^4$

= 16 subsets

Therefore, option (5) is false.

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