Question

give an example of two sets that meet the given conditions. if the conditions are impossible to satisfy, explain why. the two sets are neither equivalent nor equal. choose the correct answer below. a. ( a = {1, 2, 3, 4, 5} ) and ( b = {100, 200} ) b. the conditions are impossible to satisfy, since any two sets must either be equivalent or equal c. ( a = {1, 2, 3, 4, 5} ) and ( b = {5, 3, 1, 2, 4} ) d. ( a = {1, 2, 3, 4, 5} ) and ( b = {100, 200, 300, 400, 500} )

Explanation:

First, define key terms: Equal sets have identical elements; equivalent sets have the same number of elements (same cardinality).

• Option C: Sets A and B have identical elements, so they are equal (and thus equivalent), violating the condition.
• Option D: Both sets have 5 elements, so they are equivalent (not equal, but still fail the "neither equivalent nor equal" rule).
• Option B is wrong because sets can have different cardinalities and different elements, making them neither equivalent nor equal.
• Option A: Set A has 5 elements, set B has 2 elements (different cardinality, so not equivalent), and no shared elements (so not equal), satisfying the condition.

Answer:

A. $A=\{1, 2, 3, 4, 5\}$ and $B=\{100, 200\}$