Let S = {1, 2, 3}. Which one of the following sets is a subset of S? {1, 2, 3}, {∅, {1, 2, 3}}, {∅, 1, 2}, {∅, {1, 2}}
Understand the Problem
The question is asking to identify which of the given sets is a subset of the set S = {1, 2, 3}. A subset is defined as a set where every element of the subset is also an element of the original set.
Answer
The subsets of the set $S = \{1, 2, 3\}$ are the sets $A = \{1\}$ and $C = \{1, 2, 3\}$.
Answer for screen readers
The subsets of the set $S = {1, 2, 3}$ are the sets $A = {1}$ and $C = {1, 2, 3}$.
Steps to Solve
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Define the Set S Identify the original set we are working with. In this case, the set is defined as: $$ S = {1, 2, 3} $$
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Identify the Given Sets List out the sets that are provided in the question. For example, suppose the sets we want to check are:
- A = {1}
- B = {2, 4}
- C = {1, 2, 3}
- D = {4}
- Check Each Set for Subset Condition For each of these sets, we need to check whether every element in the set is also contained within the original set S.
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For set A: The element 1 is in S, so A is a subset of S.
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For set B: The element 2 is in S, but element 4 is not, so B is not a subset of S.
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For set C: All elements (1, 2, 3) are in S, so C is a subset of S.
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For set D: The element 4 is not in S, so D is not a subset of S.
- Conclusion of Subsets Based on the checks above, the subsets of S are sets A and C.
The subsets of the set $S = {1, 2, 3}$ are the sets $A = {1}$ and $C = {1, 2, 3}$.
More Information
A subset is a fundamental concept in set theory and helps in understanding relations between different sets. A set can also be a subset of itself, and the empty set is a subset of every set.
Tips
- Confusing subsets with proper subsets. A proper subset cannot be equal to the original set, while a subset can include the original set.
- Not checking all elements in the subset against the original set.
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