🧠 logic

1. The problem asks for the number of rows in truth tables for given compound propositions. 2. The number of rows in a truth table is $2^n$ where $n$ is the number of distinct prop

1. **Problem:** Construct truth tables for each compound proposition: a) $p \to \neg p$, b) $p \leftrightarrow \neg p$, c) $p \oplus (p \lor q)$, d) $(p \land q) \to (p \lor q)$, e

1. The problem asks to verify logical equivalences and simplify logical expressions. (a) Show that $ (p \lor q) \to p $ is logically equivalent to $ (\sim p \land \sim q) \lor p $

1. Énonçons le problème : Nous avons la proposition \(R\) suivante : \((\forall x \in \mathbb{R})[x^2 = 25 \to x = 5]\).

1. **State the problem:** Construct a truth table for the compound proposition $p \to \neg p$. 2. **Recall definitions:**

1. Problem: Construct a truth table for the compound proposition $p \to \neg p$.\n\n2. Recall that $p \to q$ (implication) is false only when $p$ is true and $q$ is false; otherwis

1. The problem is to construct a truth table for the compound proposition $p \wedge \neg p$. 2. First, list all possible truth values for $p$. Since $p$ is a simple proposition, it

1. **Problem Statement:** Construct the truth table for the compound proposition $p \to \neg q$. 2. **Identify variables:** The proposition involves two variables: $p$ and $q$.

1. We need to construct the truth table for the compound proposition $p \oplus p$ where $\oplus$ denotes the exclusive OR (XOR) operation. 2. Recall the XOR truth table: $A \oplus

1. The problem asks to express logical propositions in English based on the given propositions: - $p$: I bought a lottery ticket this week.

1. **State the problem:** Identify which sentences are propositions and determine the truth value of each proposition. 2. **Definition:** A proposition is a declarative sentence th

1. **Stating the problem:** Construct truth tables for statements 6, 17, 14, and 21 and replace T/F with 1/0. 2. **Step 1: Statement 6a:** "Stocks are increasing but interest rates

1. **State the problem:** Prove the argument is valid: "All mathematicians are logical."

1. The problem asks us to express the given statements in symbolic form. 2. For i) "Some students can not appear in exam":

1. **State the problem:** We need to use the indirect method (proof by contradiction) to derive $\neg q$ from the premises:

1. **State the problems:** We want to verify the logical equivalences:

1. The given words are: CAT, PUT, LET, BUN, WIN. 2. Arrange them in reverse alphabetical order:

1. **State the problem:** Given the sequence of letters `C L R T B Q S M A P D I N F J K G Y X`, we remove all vowels and then find the 13th letter from the left end in the remaini

1. For part (a): - Problem: "Linda owns a red convertible, and everyone who owns a red convertible has gotten at least one speeding ticket. Prove that someone in this class has got

1. For part (a): - Given: Linda owns a red convertible.

1. The problem asks to find the contrapositive of the statement: "If P, then Q". 2. Recall that the contrapositive of a statement "If P, then Q" is always "If not Q, then not P".