Answered

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\begin{tabular}{|l|l|}
\hline
(a) [tex]$A$[/tex] is the set of even numbers greater than 15 and less than 21. & \\
[tex]$B$[/tex] is the set of integers greater than 3 and less than 7. & \begin{tabular}{l}
0 equivalent but not equal \\
0 equal but not equivalent \\
0 both equivalent and equal \\
0 neither equivalent nor equal \\
\end{tabular} \\
\hline
(b) [tex]$A=\{75,76,77,78\}$[/tex] & 0 equivalent but not equal \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Let's solve the given question step-by-step based on the descriptions provided.

### Part (b)

Sets Definition:
1. Set [tex]\( A \)[/tex] is the set of even numbers greater than 15 and less than 21.
2. Set [tex]\( B \)[/tex] is the set of integers greater than 3 and less than 7.

Determine Set [tex]\( A \)[/tex]:
- The even numbers greater than 15 and less than 21 are {16, 18, 20}.
- Therefore, [tex]\( A = \{16, 18, 20\} \)[/tex].

Determine Set [tex]\( B \)[/tex]:
- The integers greater than 3 and less than 7 are {4, 5, 6}.
- Therefore, [tex]\( B = \{4, 5, 6\} \)[/tex].

Equality and Equivalence:
- Two sets are equal if they contain exactly the same elements.
- Two sets are equivalent if they have the same number of elements, regardless of what those elements are.

For sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- The sets [tex]\( \{16, 18, 20\} \)[/tex] and [tex]\( \{4, 5, 6\} \)[/tex] clearly do not have any common elements, so they are not equal.
- However, both sets have three elements, which makes them equivalent.

Therefore, the answer for part (b) is: 0 equivalent but not equal

### Part (c)

Sets Definition:
1. Set [tex]\( A = \{75, 76, 77, 78\} \)[/tex].

Information regarding set [tex]\( B \)[/tex] in part (c) is not provided explicitly in the table.

Since set [tex]\( B \)[/tex] in part (c) is not provided and there is no further context or numbers given for comparison, there is not enough information to answer part (c) accurately. It would require additional data about [tex]\( B \)[/tex] to make any determination on equality or equivalence relative to set [tex]\( A \)[/tex].

Considering the question framework provided in the table context, it might be reasonable to focus on the provided instructions only for part (b) and await clarification or additional data for part (c).

Hence for part (c), we cannot ascertain any specific comparison or answer without further information.

### Conclusion

- (b) [tex]\( A \)[/tex] is the set of even numbers greater than 15 and less than 21, [tex]\( B \)[/tex] is the set of integers greater than 3 and less than 7: [tex]\( 0 \)[/tex] equivalent but not equal.
- (c) Without further context or information on set [tex]\( B \)[/tex], we cannot determine an answer for set [tex]\( A = \{75, 76, 77, 78\} \)[/tex].
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