Question

Determine if these two sets are equal or equivalent. A = {2, 6, 10, 14}B = {6, 2, 14, 16}
A. Equal.
B. Equivalent.

Answer 1

concept : Two sets A and B are said disjoint sets only when intersection of A and B becomes empty set or null set.

e.g., if A and B are two sets then they are disjoint sets when .

now come to the question,

Let us assume, A = {2, 6, 10, 14}

And, B = {3, 7, 11, 15}

then,  = {2, 6, 10, 14}  {3, 7, 11, 15}

=  

here we get, A intersection B =  

so, given sets are disjoint sets.

hence, the statement is true.

Answer 2

Answer:

Equivalent

Given:

A = {2, 6, 10, 14}B = {6, 2, 14, 16}

To find:

Determine if these two sets are equal or equivalent.

Solution:

Equal Set is defined as two sets having the same elements. Two sets A and B can be equal only on the condition that each element of set A is also the element of set B.

In order to be a equivalent set the sets should possess the same cardinality. i.e it can be stated that the two sets remain equivalent to each other if only the number of elements in both the sets remain equal. The sets don't need to hold the same elements.

Given that

A = {2, 6, 10, 14}B = {6, 2, 14, 16}

It is shown that set A and B doesn't have the same elements but do have the same number of elements. So A and B are equivalent.

Conclusion:

Set A and B are equivalent.

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