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.