Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Let [tex]$A=\{83, 27, 68, 19, 34, 42, 30\}$[/tex]. Which of the following sets is a subset of [tex]$A$[/tex]?

A. [tex]F=\{64, 27, 30, 42, 34, 19\}[/tex]
B. [tex]C=\{34, 27, 83, 42, 49, 19, 30, 68\}[/tex]
C. [tex]E=\{30, 83, 34, 27, 68, 42\}[/tex]
D. [tex]D=\{72, 30, 19, 27, 68, 42, 34\}[/tex]


Sagot :

To determine which of the given sets is a subset of [tex]\( A \)[/tex], we must check if every element of each set is also an element of [tex]\( A \)[/tex]. Let's consider each set one by one:

1. Set [tex]\( F = \{64, 27, 30, 42, 34, 19\} \)[/tex]:
- Elements of [tex]\( F \)[/tex] are [tex]\( 64, 27, 30, 42, 34, 19 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 64 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( F \)[/tex] cannot be a subset of [tex]\( A \)[/tex].

2. Set [tex]\( C = \{34, 27, 83, 42, 49, 19, 30, 68\} \)[/tex]:
- Elements of [tex]\( C \)[/tex] are [tex]\( 34, 27, 83, 42, 49, 19, 30, 68 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 49 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( C \)[/tex] cannot be a subset of [tex]\( A \)[/tex].

3. Set [tex]\( E = \{30, 83, 34, 27, 68, 42\} \)[/tex]:
- Elements of [tex]\( E \)[/tex] are [tex]\( 30, 83, 34, 27, 68, 42 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- All elements of [tex]\( E \)[/tex] ([tex]\( 30, 83, 34, 27, 68, 42 \)[/tex]) are in [tex]\( A \)[/tex], so [tex]\( E \)[/tex] is indeed a subset of [tex]\( A \)[/tex].

4. Set [tex]\( D = \{72, 30, 19, 27, 68, 42, 34\} \)[/tex]:
- Elements of [tex]\( D \)[/tex] are [tex]\( 72, 30, 19, 27, 68, 42, 34 \)[/tex].
- Compare each element with set [tex]\( A = \{83, 27, 68, 19, 34, 42, 30\} \)[/tex].
- [tex]\( 72 \)[/tex] is not in [tex]\( A \)[/tex], so [tex]\( D \)[/tex] cannot be a subset of [tex]\( A \)[/tex].

After comparing all given sets with [tex]\( A \)[/tex], the only set that is a subset of [tex]\( A \)[/tex] is [tex]\( E \)[/tex].

Hence, the set [tex]\( E = \{30, 83, 34, 27, 68, 42\} \)[/tex] is a subset of [tex]\( A \)[/tex].
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.