Subjects set theory

Subset Check 2Ebb92

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1. **State the problem:** We are given three sets of states: $$K = \{DE, FL, NJ, NY, PA\}$$ $$L = \{DE, FL, GA, NJ, NY, PA\}$$ $$M = \{FL, NJ, NY, OR, PA\}$$ We need to determine if $K$ is a subset of $L$, denoted as $K \subseteq L$. 2. **Recall the definition of subset:** A set $A$ is a subset of set $B$ if every element of $A$ is also an element of $B$. Formally, $$A \subseteq B \iff \forall x (x \in A \implies x \in B)$$ 3. **Check each element of $K$ in $L$:** - $DE \in L$? Yes. - $FL \in L$? Yes. - $NJ \in L$? Yes. - $NY \in L$? Yes. - $PA \in L$? Yes. 4. **Conclusion:** Since every element of $K$ is in $L$, we have $$K \subseteq L$$ **Final answer:** Yes, $K$ is a subset of $L$.