🧠 logic

1. The problem asks to translate the logical statement \(\forall x \exists y (x < y)\) into English, where the domain for each variable is all real numbers. 2. The symbol \(\forall

1. The problem asks to translate the logical statement \(\forall x \exists y (x < y)\) into English, where the domain for each variable is all real numbers. 2. The symbol \(\forall

1. The problem is to translate the logical statement $\forall x (C(x) \lor \exists y (C(y) \land F(x,y)))$ into plain English. 2. The symbol $\forall x$ means "for all $x$" or "for

1. The problem is to create a truth table for the logical expression $p \lor q \land r$. 2. According to the order of operations in logic, the AND operation ($\land$) is evaluated

1. The problem is to create a truth table for the logical expression $p \lor q \land r$. 2. According to the order of operations in logic, \textbf{AND} ($\land$) has higher precede

1. The problem is to create a truth table for the logical expression $p \lor q$ and the variable $q$. 2. The logical OR operator $\lor$ means the result is true if at least one of

1. The problem is to create a truth table for the logical expression $p \lor q$, where $\lor$ represents the logical OR operation. 2. The OR operation $p \lor q$ is true if at leas

1. The problem is to create a truth table for the logical expression $p \lor q$, where $\lor$ represents the logical OR operation. 2. The OR operation $p \lor q$ is true if at leas

1. The problem is to identify whether the given statements "2.", "3.", "4.", and "5." are truths (katotohanan) or opinions (opinyon). 2. In Filipino, "katotohanan" means a fact or

1. The problem asks for the negation of the statement $$\forall x (P(x) \to Q(x))$$. 2. Recall that the negation of a universal quantifier $$\forall x$$ is an existential quantifie

1. The problem asks for the contrapositive of the implication $ (p \lor q) \to r $. 2. Recall the contrapositive of an implication $ A \to B $ is $ \neg B \to \neg A $.

1. Problem: Write the negation, converse, inverse, and contrapositive of the implication and determine the truth value for each. 2. Definitions:

1. **Stating the problem:** We are asked to prove the validity of the logical statements Modus Ponens, Modus Tollens, and Syllogism using truth tables and negation.

1. **State the problem:** We need to identify the type of error in the argument: "All superheroes wear capes. The Masked Gomer wears a cape. Hence, The Masked Gomer is a superhero.

1. The problem is to represent the statement "All birds can fly" using logical quantifiers and predicates. 2. The predicates are:

1. **State the problem:** Construct truth tables for the following statements: a. $\left(\sim q \wedge r\right) \vee \left[p \wedge \left(q \wedge \sim r\right)\right]$

1. **State the problem:** Construct truth tables for the following statements: a. $(\sim q \wedge r) \vee [p \wedge (q \wedge \sim r)]$

1. **Problem Statement:** Identify which of the given sentences is not a proposition. 2. **Understanding Propositions:** A proposition is a declarative sentence that is either true

1. Let's restate the problem clearly: You want to write a question properly to check if it is true. 2. To do this, we need to formulate a clear mathematical or logical statement th

1. **Problem Statement:** We need to state and prove the rule of disjunction syllogism, which is a valid argument form in logic.

1. **Énoncé du problème :** On considère la proposition $P : (\forall x \in \mathbb{Z}), x^2 \in \mathbb{N} \Rightarrow x \in \mathbb{N}$.