which statements are true about x? select three options. x∈b∪c x∈b∩c x∈a∪c x∈a∩c x∈a

Answer:

1. $x\in B\cup C$
2. $x\in A\cup C$
3. $x\in A\cap C$

Explanation:

Step1: Analyze union definition

The union $B\cup C$ contains all elements in $B$ or $C$. Since $x$ is in the intersection of $B$ and $C$, it is in $B\cup C$.

Step2: Analyze union definition

The union $A\cup C$ contains all elements in $A$ or $C$. As $x$ is in the intersection of $A$ and $C$, it is in $A\cup C$.

Step3: Analyze intersection definition

The intersection $A\cap C$ contains elements in both $A$ and $C$. Clearly, $x$ is in the region where $A$ and $C$ overlap, so $x\in A\cap C$.