This is a discrete math question. This could be solved using truth table. I am just confused. I really need help to do solve this problem. ### Logical Properties and Statements**Logical Equivalences:**- **Idempotence:** - $ p \lor p \equiv p $ - $ p \land p \equiv p $- **Commutativity:** - $ p \lor q \equiv q \lor p $ - $ p \land q \equiv q \land p $- **Associativity:** - $ p \lor (q \lor r) \equiv (p \lor q) \lor r $ - $ p \land (q \land r) \equiv (p \land q) \land r $- **Distributivity:** - $ p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) $ - $ p \land (q \lor r) \equiv (p \land q) \lor (p \land r) $- **Absorptivity:** - $ p \lor (p \land q) \equiv p $ - $ p \land (p \lor q) \equiv p $- **Identity:** - $ p \lor \bot \equiv p $ - $ p \land \top \equiv p $- **Complementarity:** - $ p \lor (\neg p) \equiv \top $ - $ p \land (\neg p) \equiv \bot $- **Dominance:** - $ p \lor \top \equiv \top $ - $ p \land \bot \equiv \bot $- **Involution:** - $ \neg (\neg p) \equiv p $- **Exclusivity:** - $ \neg (\top) \equiv \bot $ - $ \neg (\bot) \equiv \top $- **DeMorgan’s:** - $ \neg (p \lor q) \equiv (\neg p) \land (\neg q) $ - $ \neg (p \land q) \equiv (\neg p) \lor (\neg q) $### Logical Inferences- **Adjunction:** - $ \frac{p Suppose that \( p, q, r $ and $ s $ are propositions. Determine if the following argument is valid using any appropriate means. Support your answer.\[\begin{align*}(p \rightarrow q) \quad (r \rightarrow s) \\\hline(p \lor r) \rightarrow (q \lor s)\end{align*}\]

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Description: This is a discrete math question. This could be solved using truth table. I am just confused. I really need help to do solve this problem. ### Logical Properties and Statements**Logical Equivalences:**- **Idempotence:** - $ p \lor p \equiv p $ -

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Answered: Suppose that p, q,r and s are…

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Suppose that p, q,r and s are propositions. Determine if the following argument is valid using any appropriate means. Support your answer. (p → q) (r → s) (p V r) → (q V s)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.5: The Format Proof Of A Theorem

Problem 11E: When can a theorem be cited as a reason reason in a proof?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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This is a discrete math question. This could be solved using truth table. I am just confused. I really need help to do solve this problem.

### Logical Properties and Statements

**Logical Equivalences:**

- **Idempotence:**
- $ p \lor p \equiv p $
- $ p \land p \equiv p $

- **Commutativity:**
- $ p \lor q \equiv q \lor p $
- $ p \land q \equiv q \land p $

- **Associativity:**
- $ p \lor (q \lor r) \equiv (p \lor q) \lor r $
- $ p \land (q \land r) \equiv (p \land q) \land r $

- **Distributivity:**
- $ p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) $
- $ p \land (q \lor r) \equiv (p \land q) \lor (p \land r) $

- **Absorptivity:**
- $ p \lor (p \land q) \equiv p $
- $ p \land (p \lor q) \equiv p $

- **Identity:**
- $ p \lor \bot \equiv p $
- $ p \land \top \equiv p $

- **Complementarity:**
- $ p \lor (\neg p) \equiv \top $
- $ p \land (\neg p) \equiv \bot $

- **Dominance:**
- $ p \lor \top \equiv \top $
- $ p \land \bot \equiv \bot $

- **Involution:**
- $ \neg (\neg p) \equiv p $

- **Exclusivity:**
- $ \neg (\top) \equiv \bot $
- $ \neg (\bot) \equiv \top $

- **DeMorgan’s:**
- $ \neg (p \lor q) \equiv (\neg p) \land (\neg q) $
- $ \neg (p \land q) \equiv (\neg p) \lor (\neg q) $

### Logical Inferences

- **Adjunction:**
- \( \frac{p

Suppose that $ p, q, r $ and $ s $ are propositions. Determine if the following argument is valid using any appropriate means. Support your answer.

\[
\begin{align*}
(p \rightarrow q) \quad (r \rightarrow s) \\
\hline
(p \lor r) \rightarrow (q \lor s)
\end{align*}
\]

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