Question

set concepts
question 30, 2.1.89
part 1 of 2
hw score: 72.5%, 29 of 40 points
points: 0 of 1
answer the following questions about the given sets.
a. are the sets equivalent? explain.
b. are the sets equal? explain.
a = {x | x∈n and 99 ≤ x ≤ 104}
b = {x | x∈n and 98 < x < 105}

a. are the sets equivalent? explain.
a. the sets are equivalent because set a does not contain the exact same elements as set b.
b. the sets are equivalent because n(a) = n(b).
c. the sets are not 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).

Explanation:

Step1: List elements of Set A

$A = \{99, 100, 101, 102, 103, 104\}$, so $n(A)=6$

Step2: List elements of Set B

$B = \{99, 100, 101, 102, 103, 104\}$, so $n(B)=6$

Step3: Analyze equivalence

Equivalent sets have equal cardinality. Since $n(A)=n(B)$, sets are equivalent.

Step4: Analyze equality

Equal sets have identical elements. $A$ and $B$ share all elements.

Answer:

a. B. The sets are equivalent because n(A) = n(B).
b. The sets are equal because they contain exactly the same elements: $\{99, 100, 101, 102, 103, 104\}$.