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The question asks to evaluate the truth value of the following logical statement:

\[
(p \iff q) \land (q \iff r)
\]

Given the conditions:
- \(p\) is **true**,
- \(q\) is **false**,
- \(r\) is **false**.

### Step 1: Evaluate \(p \iff q\)
The biconditional (\(\iff\)) is true when both sides have the same truth value.

- \(p = \text{true}\),
- \(q = \text{false}\).

Since \(p\) and \(q\) have different truth values, \(p \iff q = \text{false}\).

### Step 2: Evaluate \(q \iff r\)
- \(q = \text{false}\),
- \(r = \text{false}\).

Since both \(q\) and \(r\) are false, \(q \iff r = \text{true}\) (because both sides have the same truth value).

### Step 3: Evaluate the entire expression
The overall expression is \((p \iff q) \land (q \iff r)\).
- \(p \iff q = \text{false}\),
- \(q \iff r = \text{true}\).

The conjunction (\(\land\)) is true only if both statements are true. Since one of them is false, the entire expression evaluates to **false**.

### Final Answer:
The truth value of the given expression is **false**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the truth table for the biconditional (\(\iff\)) operator?
2. How does conjunction (\(\land\)) affect

Suppose that statement p is true, statement q is false, and statement r is false. Evaluate the truth value of: (p <=> q) ∧ (q <=> r)

Learn how to solve a logical statement involving biconditional and conjunction operators where p is true, q is false, and r is false. This problem demonstrates the application of logic rules in determining the truth value of compound statements.

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