🧠 logic

1. **State the problem:** Construct the truth table for the compound statement $ (p \to q) \lor (\neg p \land \neg q) $ and determine if it is a tautology, contradiction, or contin

1. **State the problem:** We need to determine if the logical statement $$(p \wedge q) \to p$$ is a tautology. 2. **Recall definitions:**

1. **State the problem:** We have two propositions: - $p$: I complete my homework.

1. **State the problem:** We want to find the logical equivalence of the expression $$(p \Rightarrow q) \wedge (\neg p \vee q)$$. 2. **Recall the implication equivalence:** The imp

1. The problem asks to find the logical equivalence of the expression $ (p \Rightarrow q) \wedge (\neg p \vee q) $.\n\n2. Recall that the implication $ p \Rightarrow q $ is logical

1. **State the problem:** We want to find the logical equivalence of the expression $$(p \Rightarrow q) \wedge (\neg p \vee q).$$ 2. **Recall the implication equivalence:** The imp

1. **State the problem:** Show that the logical expression $R \to \sim[(\sim R \wedge X) \lor \sim(R \lor X)]$ is a tautology. 2. **Rewrite the expression:** The expression is an i

1. **State the problem:** We are given propositions: - $p$: I bought a lottery ticket this week.

1. The problem asks to express the proposition \(\neg p\) in English. 2. Given \(p\): "I bought a lottery ticket this week."

1. **State the problem:** We need to identify which sentences are propositions and determine their truth values. 2. **Definition:** A proposition is a declarative sentence that is

1. **State the problem:** We need to determine which sentences are propositions and find the truth values of those that are propositions. 2. **Definition:** A proposition is a decl

1. The problem asks to express the exclusive disjunction $p@q$ using only negation ($\sim$), conjunction ($\wedge$), and inclusive disjunction ($\vee$). 2. By definition, $p@q$ mea

1. **State the problem:** Construct a truth table for the compound proposition $ (p \lor q) \lor r $. 2. **List all possible truth values for $p$, $q$, and $r$: Since each variable

1. **State the problem:** Construct a truth table for the compound proposition $ (p \lor q) \lor r $. 2. **List all possible truth values for $p$, $q$, and $r$: Since each variable

1. **State the problem:** Construct a truth table for the compound proposition $ (p \lor q) \lor r $. 2. **List all possible truth values for $p$, $q$, and $r$: Since each can be t

1. **Problem Statement:** Construct truth tables for the compound propositions: a) $p \oplus p$

1. The problem asks us to determine the truth value of each biconditional statement. A biconditional "if and only if" statement $p \iff q$ is true if both $p$ and $q$ have the same

1. The problem asks for the Boolean expression representing "4 greater than 5." 2. In mathematical terms, this is written as $4 > 5$.

1. The problem asks to identify the term for an argument that goes from the general to the particular. 2. In logic and reasoning, an argument that starts with a general statement o

1. The problem involves analyzing the logical expressions: 2. 1. \(\neg P \lor Q\) means either \(P\) is false or \(Q\) is true.

1. The problem asks us to determine whether each conclusion is based on inductive or deductive reasoning. 2. Inductive reasoning involves making a generalization based on specific