🧠 logic

1. The problem asks to determine whether each sentence is a proposition or not. 2. A proposition is a declarative sentence that is either true or false, but not both.

1. مسئله: اگر گزاره $(p \lor q) \Rightarrow (r \lor s)$ نادرست باشد، ارزش گزاره $p \land q$ با کدام گزاره برابر است؟ 2. فرمول و قوانین مهم:

1. **State the problem:** Construct a truth table for the compound proposition $$((\neg p \lor r) \land (p \leftrightarrow q)) \to r$$. 2. **Recall the logical operators:**

1. The statement "true or false" is a prompt asking to determine the truth value of a given proposition or statement. 2. Since no specific proposition or statement is provided, we

1. **State the problem:** We want to analyze the logical argument $[(P \to Q) \wedge \neg P] \to P$ and determine its validity. 2. **Recall the implication formula:** An implicatio

1. **State the problem:** We need to construct a complete truth table for the compound statement $$[(p \to q) \wedge (r \to \neg q)] \to (p \to \neg r)$$ and then classify it as a

1. **Problem statement:** Translate the English statements into propositional logic expressions with clear proposition definitions. 2. **Define propositions for (a):**

1. The problem is to determine which club (A, B, or C) each person works for based on given conditions. 2. To solve this, we use logical deduction and elimination rules.

1. **State the problem:** We need to analyze the logical formula $$ (p \to (p \wedge q)) \to (p \to q) $$ and determine its truth or validity.

1. **State the problem:** We need to verify the logical equivalence of the statement $$(A \to \sim A) \equiv (\sim B \to \sim A)$$.

1. **Problem Statement:** Write the converse, inverse, and contrapositive of the statement: "If we have a quiz today, then we will not have a quiz tomorrow." 2. **Recall definition

1. **Problem Statement:** Given the propositional logic statements: \(p \rightarrow q\) (if p then q) and \(p\) is true, determine the truth value of \(q\). 2. **Formula Used:** Th

1. **State the problem:** We need to find the value of the logical expression $$F = (A \text{ AND } B) \text{ OR } (A \text{ XOR } B)$$ given $$A=1$$ and $$B=0$$. 2. **Recall the l

1. **Stating the problem:** We have three statements in an advertisement: i. There are three statements in this ad.

1. The problem is to create a truth table for the logical AND operation between two propositions $p$ and $q$. 2. The AND operation, denoted as $p \wedge q$, is true only when both

1. The problem is to create a truth table for the logical AND operation between two propositions $p$ and $q$. 2. The AND operation, denoted as $p \wedge q$, is true only when both

1. **Problem:** Elephants have cells in their bodies, and all cells have DNA. Therefore, what can we conclude? 2. **Problem:** All horses have manes. The Appaloosa is a horse; ther

1. The problem asks to identify the correct definition among the given options about logical statements. 2. Important definitions in logic:

1. The problem asks to identify the correct definition among the given options about logical statements. 2. Let's review the definitions:

1. The problem asks to express the quantification \(\exists x \exists y P(x,y)\) in English. 2. The predicate \(P(x,y)\) means "Student \(x\) has taken class \(y\)." The domain for

1. The problem asks to express the quantification \(\exists x \exists y P(x,y)\) in English. 2. The predicate \(P(x,y)\) means "Student \(x\) has taken class \(y\)." The domain for