Question: Prove that the following clause is a true constant clause: $ (p \wedge (p \Rightarrow q)) \Rightarrow q $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p …
Clause - Set
[QAZ] Prove that the following clause is a true constant clause: $ p \Rightarrow (q \Rightarrow p) $
Question: Prove that the following clause is a true constant clause: $ p \Rightarrow (q \Rightarrow p) $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p \wedge bar …
[QAZ] Prove that the following clause is a true constant clause: $ p \Rightarrow (p \vee q) $
Question: Prove that the following clause is a true constant clause: $ p \Rightarrow (p \vee q) $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p \wedge bar …
[QAZ] Prove that there is no largest prime number. (or: Prove that the set of primes is an infinite set)
Question: Prove that there is no largest prime number. (or: Prove that the set of primes is an infinite set) Answer Assuming $ {P_n} $ is the largest prime number, we call p the product of n known prime numbers: $ \begin {array} {l} p = {p_1} {p_2} .. .. {p_n} \\ \end {array} $ …
[QAZ] Prove that the following equation has no integral solution $ 15x ^ 2 – 7y ^ 2 = 9 $
Question: Prove that the following equation has no integral solution $ 15x ^ 2 – 7y ^ 2 = 9 $ Answer Suppose (1) has an integral solution $ x = n, y = m; n, m \in Z $ Therefore: $ 15 {n ^ 2} – 7 {m ^ 2} = 9 (2) $ …
[QAZ] Prove that the following equation has no integral solution $ 15x ^ 2 – 7y ^ 2 = 9 $Read More
[QAZ] Which of the following statements is a proposition? If it is a proposition to consider true (D) false (S)? A) & quot; Number 77 is a prime number & quot; b) & quot; Quadrilateral with equal and opposite sides is parallelogram & quot; c) & quot; -a is some sounds & quot;
Question: Which of the following statements is a proposition? If it is a proposition to consider true (D) false (S)? A) & quot; Number 77 is a prime number & quot; b) & quot; Quadrilateral with equal and opposite sides is parallelogram & quot; c) & quot; -a is some sounds & quot; Answer a) …
[QAZ] Prove that there cannot be two integers m and n so that the following equation is satisfied: $ 2m ^ {2} + n ^ {2} = 2007 $.
Question: Prove that there cannot be two integers m and n so that the following equation is satisfied: $ 2m ^ {2} + n ^ {2} = 2007 $. Answer Assuming there are two integers $ m $, $ n $ so: $ 2m ^ 2 + n ^ 2 = 2007 $ (*) Since …
[QAZ] For set \(A = \left \{{a, b, c, d} \right \}, B = \left \{{b, d, e} \right \}, C = \left \{{a, b, e} \right \} \). Proof: 1) \(A \cap (B \setminus C) = (A \cap B) \setminus (A \cap C) \) 2) \(A \setminus (B \cap C) = (A \setminus B) \cup (A \setminus C) \).
Question: For set \(A = \left \{{a, b, c, d} \right \}, B = \left \{{b, d, e} \right \}, C = \left \{{a, b, e} \right \} \). Proof: 1) \(A \cap (B \setminus C) = (A \cap B) \setminus (A \cap C) \) 2) \(A \setminus (B \cap C) = (A \setminus B) …
[QAZ] Prove that: $ p \Rightarrow (q \Rightarrow r) \equiv (p \wedge q) \Rightarrow r $
Question: Prove that: $ p \Rightarrow (q \Rightarrow r) \equiv (p \wedge q) \Rightarrow r $ Answer We have: $ \begin {array} {l} p \Rightarrow \left ({q \Rightarrow r} \right) \equiv \bar p \vee \left ({q \Rightarrow r} \right) \\ \equiv \bar p \left ({\bar q \vee r} \right) \\< br> \equiv \left ({\bar p …
[QAZ] Prove that: $ p \Rightarrow (q \Rightarrow r) \equiv (p \wedge q) \Rightarrow r $Read More
[QAZ] Prove that the following clause is a true constant clause: $ (p \wedge q) \Rightarrow p $
Question: Prove that the following clause is a true constant clause: $ (p \wedge q) \Rightarrow p $ Answer Based on the formulas: $ \begin {array} {l} p \Rightarrow q \equiv \bar p \vee q \\ p \wedge q \equiv \bar p \vee \bar q \\ \bar p \Rightarrow \bar q \equiv p \wedge bar …