Subjects set theory

Subset Check

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Subset Check


1. **State the problem:** We have two sets: - $A = \{x \mid x \text{ is an even number less than } 10\}$ - $B = \{2, 4, 6, 8, 10\}$ The question asks if $A \subseteq B$, that is if every element in $A$ is also in $B$. 2. **List the elements of $A$:** Since $A$ is the set of even numbers less than 10, we have: $$A = \{2, 4, 6, 8\}$$ 3. **Compare elements of $A$ with elements of $B$:** - $2 \in B$ - $4 \in B$ - $6 \in B$ - $8 \in B$ 4. **Check if all elements of $A$ are in $B$:** Yes, all of $A$'s elements (2, 4, 6, 8) are contained in $B$. 5. **Conclusion:** Since every element of $A$ is in $B$, the statement $A \subseteq B$ is **True**. **Final answer:** True