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Answered

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Which is a subset of [tex]\{1, 2, 4, 5, 6\}[/tex]?

A. [tex]\{5, 6, 7\}[/tex]
B. [tex]\{0, 1, 2\}[/tex]
C. [tex]\{3, 4\}[/tex]
D. [tex]\{2, 6\}[/tex]

Sagot :

GinnyAnsweridn
To determine which sets are subsets of the main set [tex]\(\{1, 2, 4, 5, 6\}\)[/tex], we need to verify if all elements of each subset are present in the main set.

1. Checking the set [tex]\((5, 6, 7)\)[/tex]:
- Elements to check: 5, 6, 7
- 5 and 6 are present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- 7 is not present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- Therefore, [tex]\((5, 6, 7)\)[/tex] is not a subset of [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].

2. Checking the set [tex]\((0, 1, 2)\)[/tex]:
- Elements to check: 0, 1, 2
- 1 and 2 are present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- 0 is not present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- Therefore, [tex]\((0, 1, 2)\)[/tex] is not a subset of [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].

3. Checking the set [tex]\((3, 4)\)[/tex]:
- Elements to check: 3, 4
- 4 is present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- 3 is not present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- Therefore, [tex]\((3, 4)\)[/tex] is not a subset of [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].

4. Checking the set [tex]\((2, 6)\)[/tex]:
- Elements to check: 2, 6
- Both 2 and 6 are present in [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
- Therefore, [tex]\((2, 6)\)[/tex] is a subset of [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].

Conclusively, only the set [tex]\((2, 6)\)[/tex] is a subset of [tex]\(\{1, 2, 4, 5, 6\}\)[/tex].
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