Question

for each pair of sets, choose the best description.
pair of sets\tdescription
(a) $a = \\{h, j, k, m\\}$
$b = \\{h, q, u, j\\}$
\t$\bigcirc$ equivalent but not equal
\t$\bigcirc$ equal but not equivalent
\t$\bigcirc$ both equivalent and equal
\t$\bigcirc$ neither equivalent nor equal
(b) $a$ is the set of integers greater than 15 and less than 19.
$b$ is the set of integers greater than 15.
\t$\bigcirc$ equivalent but not equal
\t$\bigcirc$ equal but not equivalent
\t$\bigcirc$ both equivalent and equal
\t$\bigcirc$ neither equivalent nor equal
(c) $a = \\{53, 52, 51\\}$
$b = \\{51, 52, 53\\}$
\t$\bigcirc$ equivalent but not equal
\t$\bigcirc$ equal but not equivalent
\t$\bigcirc$ both equivalent and equal
\t$\bigcirc$ neither equivalent nor equal
(d) $a$ is the set of odd numbers greater than 2 and less than 10.
$b = \\{22, 23, 24\\}$
\t$\bigcirc$ equivalent but not equal
\t$\bigcirc$ equal but not equivalent
\t$\bigcirc$ both equivalent and equal
\t$\bigcirc$ neither equivalent nor equal

Explanation:

Step1: Define key terms

• Equal sets: Same elements (order doesn't matter).
• Equivalent sets: Same number of elements (cardinality).

Step2: Analyze pair (a)

Count elements: $n(A)=4$, $n(B)=4$ (equivalent).
Elements differ ($k,m
eq q,u$) (not equal).
Conclusion: equivalent but not equal.

Step3: Analyze pair (b)

Set $A=\{16,17,18\}$ ($n(A)=3$).
Set $B=\{16,17,18,...\}$ (infinite, $n(B)
eq3$).
Conclusion: neither equivalent nor equal.

Step4: Analyze pair (c)

Sets have identical elements (order doesn't matter, so equal).
Equal sets are always equivalent.
Conclusion: both equivalent and equal.

Step5: Analyze pair (d)

Set $A=\{3,5,7,9\}$ ($n(A)=4$).
Set $B=\{22,23,24\}$ ($n(B)=3$) (not equivalent).
Elements are entirely different (not equal).
Conclusion: neither equivalent nor equal.

Answer:

(a) equivalent but not equal
(b) neither equivalent nor equal
(c) both equivalent and equal
(d) neither equivalent nor equal