🧠 logic

1. The problem gives two propositions: $p$: "Swimming at the New Jersey shore is allowed" and $q$: "Sharks have been spotted near the shore." 2. We are asked to interpret the comp

1. The problem statement involves understanding the logical implications denoted by the arrows → in the expressions $p \to q$ and $q \to p$. 2. In logic, $p \to q$ means "if p, the

1. **State the problem:** We need to represent the sentence "She is not good in math and she is not doing well in English implies she will not pass the exam" in symbolic form using

1. Problem statement: We need to find the symbolic compound statement for "If she will not pass the exams, then she is sad if and only if she is not good in math or she is not doin

1. The problem is to solve a logical expression or determine its truth values using a truth table. 2. To proceed, we first need a specific logical expression or statement (e.g., $p

1. State the problem: Verify De Morgan's Law $$\sim (p \wedge q) \equiv \sim p \vee \sim q$$ indicates that the negation of a conjunction is logically equivalent to the disjunction

1. **State the problem:** We have logical propositions:

1. Let's first understand what a contingency is. A contingency is a statement that is neither always true (tautology) nor always false (contradiction).

1. The user states "nope not b or c" which implies eliminating options b and c from a set of choices. 2. Since the specific problem or question context is missing, I interpret this

1. The problem asks to solve the expression $M \wedge N$ in a truth table, where $\wedge$ represents the AND operation. 2. The AND operation outputs true only if both inputs are tr

1. The problem is to solve or analyze logical expressions using a truth table. 2. A truth table systematically lists all possible truth values of variables and shows the result of

1. The problem is to create a truth table for the logical expression $m \wedge n$, where $\wedge$ is the AND operator. 2. The AND operator is true only if both operands are true.

1. The problem is to construct the truth table for a logical expression or variable(s). 2. A truth table enumerates all possible truth values of variables and the result of the log

1. The problem asks to identify whether $[(p \to q) \lor (q \to r) \lor (r \to p)]$ is a tautology, contradiction, or contingency. 2. The problem also asks to identify whether $[((

1. The problem is to understand and simplify the expression $P \equiv (\sim r^{\sim q})$. 2. Typically, the symbol $\sim$ denotes negation (NOT), and $^$ sometimes represents XOR o

1. The problem is to simplify and understand the expression $P \equiv (\sim r^{\sim q})$. 2. The expression uses the notation $\sim$ typically meaning negation, but the caret symbo

1. **State the problem:** Simplify and understand the logical expression $P \equiv (\sim r \wedge \sim q)$. 2. **Recall definitions:** $\sim r$ means NOT $r$, and $\wedge$ means AN

1. We need to prove the logical equivalence using truth tables. 2. For the first formula, De Morgan's law states: $$\neg (P \wedge Q) = \neg P \vee \neg Q$$. We construct the truth

1. Construct the truth tables for the given propositions. **i.** $\sim p \lor q$

1. The question "So true or false" is a request for evaluation of a statement's truth value. 2. However, no specific statement or proposition has been given to evaluate.

1. The problem is to construct complete truth tables for the given logical statements involving propositions P, Q, and R. 2. Define the propositions: