p V (q ^r) in a truth table

p is false
q is true
r is false

Let's break down the logical expression \( p \vee (q \land r) \) and evaluate it step by step, given that:

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

We need to calculate the expression using the following logical operators:

- \( \vee \): OR
- \( \land \): AND

### Step-by-step evaluation:
1. **Evaluate \( q \land r \):**
   \[
   q \land r = \text{true} \land \text{false} = \text{false}
   \]
   (AND requires both operands to be true, so the result is false.)

2. **Evaluate \( p \vee (q \land r) \):**
   \[
   p \vee \text{false} = \text{false} \vee \text{false} = \text{false}
   \]
   (OR requires at least one operand to be true, but both are false, so the result is false.)

Thus, the final result of \( p \vee (q \land r) \) is **false**.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What happens if \( p \) is true in this expression?
2. How does the truth table for \( q \land r \) look?
3. Can you explain the difference between \( \vee \) (OR) and \( \land \) (AND)?
4. What if \( r \) were true instead of false—how would that affect the result?
5. How does this type of logical expression apply to real-world situations, such as decision-making?

**Tip:** When working with logical operators, remember that AND requires both operands to be true, while OR only requires one.

p V (q ^ r) in a truth table; p is false, q is true, r is false.

Learn how to evaluate the logical expression p ∨ (q ∧ r) using truth tables. This problem involves understanding logical operators (AND, OR) and applying them step by step, including p=false, q=true, r=false. Suitable for students in Grades 9-12 studying basic logic and truth tables.

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