Question

answer the following questions about the given sets.
a. are the sets equivalent? explain.
b. are the sets equal? explain.
a = {8, 8, 8, 9, 9, 10, 10, 10}
b = {10, 9, 8}
c. the sets are equivalent because set a does not contain the exact same elements as set b.
d. the sets are not equivalent because n(a) ≠ n(b).
b. are the sets equal? explain.
a. the sets are not equal because set a contains the exact same elements as set b.
b. the sets are equal because n(a) = n(b).
c. the sets are not equal because n(a) ≠ n(b).
d. the sets are equal because set a contains the exact same elements as set b.

Explanation:

Step1: Define equivalent sets

Equivalent sets have equal cardinality (number of distinct elements, or total elements for multiset? No, standard sets ignore duplicates: for set $A$, distinct elements are $\{8,9,10\}$, so $n(A)=3$; $n(B)=3$.

Step2: Check equivalence

Since $n(A)=n(B)=3$, sets are equivalent.

Step3: Define equal sets

Equal sets have identical elements (order doesn't matter, duplicates don't count in standard sets).

Step4: Check equality

Set $A$ (distinct elements $\{8,9,10\}$) and set $B=\{10,9,8\}$ have identical elements.

Answer:

a. The sets are equivalent because $n(A)=n(B)=3$ (distinct elements count). Correct reasoning matches the logic that equivalent sets have the same number of elements.
b. D. The sets are equal because set A contains the exact same elements as set B.