venn diagrams
which statements are true about x? choose three correct answers.
$x \in a \cup c$
$x \in a \cap c$
$x \in b \cap c$
$x \in a$
$x \in b \cup c$

Question

Accepted Answer

# Explanation:
## Step1: Analyze $ x \in A \cup C $
The union $ A \cup C $ includes all elements in $ A $, in $ C $, or in both. From the Venn diagram, $ x $ is in the intersection of $ B $ and $ C $, and also in $ C $. Since $ C $ is part of $ A \cup C $, $ x \in A \cup C $ is true.

## Step2: Analyze $ x \in A \cap C $
The intersection $ A \cap C $ includes elements in both $ A $ and $ C $. From the diagram, $ x $ is in $ B \cap C $, not in $ A $, so $ x
otin A \cap C $, this statement is false.

## Step3: Analyze $ x \in B \cap C $
The intersection $ B \cap C $ includes elements in both $ B $ and $ C $. From the diagram, $ x $ is in the overlapping region of $ B $ and $ C $, so $ x \in B \cap C $ is true.

## Step4: Analyze $ x \in A $
From the diagram, $ x $ is in $ B \cap C $, not in $ A $, so $ x
otin A $, this statement is false.

## Step5: Analyze $ x \in B \cup C $
The union $ B \cup C $ includes all elements in $ B $, in $ C $, or in both. Since $ x $ is in $ B \cap C $ (so in both $ B $ and $ C $), $ x \in B \cup C $ is true.

# Answer:
The three correct statements are:
- $ x \in A \cup C $
- $ x \in B \cap C $
- $ x \in B \cup C $

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze \( x \in A \cup C \)

Step2: Analyze \( x \in A \cap C \)

Step3: Analyze \( x \in B \cap C \)

Step4: Analyze \( x \in A \)

Step5: Analyze \( x \in B \cup C \)

Answer: