🧠 logic

1. **Stating the problem:** We have several expressions and need to identify which are designations (non-propositional expressions) and which are propositions (statements that can

1. The statement to evaluate is: "Jim's mother knew that he had eaten chocolate." 2. This is a true/false question, so we need to determine if the statement is logically true or fa

1. The problem is to determine which statements are true. Since no specific statements are provided, I cannot evaluate their truthfulness. 2. To solve such problems, you need the e

1. The problem asks to identify which sentences are statements and which are not, and explain why. 2. A statement is a sentence that is either true or false, but not both.

1. The problem is to create a truth table, which is a table showing all possible truth values of logical variables and their resulting expressions. 2. To build a truth table, list

1. The problem asks to write the symbolic form of the statement: "If it’s your bday or there will be cake, then there will be cake." 2. Let $p$ represent "it’s your bday" and $q$ r

1. The problem asks to determine which statement is true, but no specific statements are provided. 2. To answer such a question, we need the list of statements to evaluate their tr

1. The problem is to determine which items match to which ones, but since no specific items or context are given, we cannot directly match anything. 2. To solve a matching problem,

1. **State the problem:** Determine whose reasoning is correct based on the information that birds are sensitive to nest disturbance and may abandon their nests if disturbed. 2. **

1. **State the problem:** We have 8 people (4 girls: Bella, Ruby, Kinsley, Samantha; 4 boys: Howard, Stanley, Chris, Mario) sitting evenly spaced around a circular table. 2. **Give

1. The user asks "so which of it is true" but does not provide any specific statements or context to evaluate. 2. To determine truth, we need clear propositions or statements to an

1. **State the problem:** Show using absorption properties that the statement $$56 (p \wedge \neg 2) \wedge (p \wedge \neg 2) \vee (2 \wedge \neg r) \leftrightarrow (p \wedge \neg

1. The problem is to identify the letter tile at the bottom-left position from the given grid of letter tiles with subscripts indicating point values. 2. The grid is described as t

1. **State the problem:** We have five boxes labeled A, B, C, D, E, each containing a unique number from 1 to 5. Given clues: - Number in A is smaller than number in C.

1. **State the problem:** We want to analyze the logical implication $(P \wedge q) \Rightarrow (P \vee \overline{q})$.

1. The problem is to choose one or more options from a list: a, b, c, or d. 2. Since the problem is about selection and does not involve a mathematical formula or calculation, the

1. نبدأ ببيان المشكلة: لدينا العبارة المنطقية $P \wedge \sim P$ ونريد معرفة ماذا تمثل. 2. الصيغة المستخدمة: $P$ تمثل عبارة منطقية يمكن أن تكون صحيحة أو خاطئة، و$\sim P$ تعني نفي $P

1. **Problem:** Show that the proposition $ (p \Rightarrow q) \Rightarrow \neg (p \wedge \neg q) $ is a tautology. 2. **Recall the definitions:**

1. **Problem:** Given the premises $(A \lor C) \to \neg D$ and $A \lor C$, prove $\neg D$. 2. **Rule of inference:** This is an example of *Modus Ponens*, which states that if $p \

1. **State the problem:** We want to analyze the logical equivalence of the statement $$[r \to (p \lor q)] \leftrightarrow \sim[r \to (r \lor q)]$$.

1. **State the problem:** Given the truth values $A = \text{false}$, $B = \text{true}$, $C = \text{false}$, and $D = \text{true}$, find the truth value of the statement: