Question 6 sm .Show that each of these conditional statements is a tautology by using truth tables. [¬p ∧ (p ∨ q)] → q
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Question 6 sm
.Show that each of these conditional statements is a tautology by using truth tables.
[¬p ∧ (p ∨ q)] → q
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- Show that each of these conditional statements is a tautology. Please show each step and the laws you use. 1) ¬p→(p→q) 2) (p∧q)→(p→q) Example: (p∧q)→p ≡¬(p∧q)∨p [Identity of implies] ≡(¬p∨¬q)∨p [De Morgan’s law] ≡(¬p∨p)∨¬q [Associative law] ≡T∨¬q [Negation law] ≡T [Domination law]Determine whether or not the following statement is a tautology or not and give reasoning. If you need to, you can build a truth table to answer this question. (q→p)∨(∼q→∼p) A. This is a tautology because it is always true for all truth values of p and q. B. This is not a tautology because it is always false for all truth values of p and q. C. This is a tautology because it is not always false for all values of p and q. D. This is not a tautology becasue it is not always true for all truth values of p and q.Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’ throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to n atoms.(d) State the number of rows in a truth table for proving the extension
- Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to natoms.(d) State the number of rows in a truth table for proving the extension.Determine whether the following proposition is a tautology: (¬p∨¬(r⟶q))⟷(p⟶(¬q∧r)) can i get a non handwriting answer so it would be easy to copy pleaseLet P(x) be the statement “x can speak Russian” and let Q(x) be the statement “x knows C++”. Express each of these statements in terms P(x), Q(x), quantifiers and logical connectives. The domain for quantifiers consists of all students at Mines. There is a student at Mines who can speak Russian and who knows C++. Every student at your school either can speak Russian or knows C++.
- This question was on a homework assignment which I could not complete before the deadline. Show that whether the following propositions is a tautology, satisfiable but not a tautology, or a contradiction. If it is a tautology or a contradiction, please give the proof. If it is satisfiable, please give a true assignment and a false assignment. (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ D) ∧ (A ∨ ¬C ∨ ¬D) ∧ (¬A ∨ ¬B ∨ ¬D) ∧ (A ∨ B ∨ ¬D)Please written by computer source 1) Write truth tables for the statement forms in A.∼p ∧ q B. p ∧ (q ∧ r) 2) Determine whether the statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. 1. p ∨ (p ∧ q) and p 2. p ∨ t and t 3. (p ∧ q) ∧ r and p ∧ (q ∧ r) 4. (p ∧ q) ∨ r and p ∧ (q ∨ r) 3) Assume x is a particular real number and use De Morgan’s laws to write negations for the statements 1. −2 < x < 7 2. x < 2 or x > 5 3. 1 > x ≥ −3 4) Use truth tables to establish which of the statement forms are tautologies and which are contradictions. 1. (p ∧ q) ∨ (∼p ∨ (p ∧ ∼q)) 2. (p ∧ ∼q) ∧ (∼p ∨ q) 5) In the below, a logical equivalence is derived from Theorem 2.1.1. Supply a reason for each step. (p ∧ ∼q) ∨ (p ∧ q) ≡ p ∧ (∼q ∨ q) by (a) ≡ p ∧ (q ∨ ∼q) by (b) ≡ p ∧ t by (c) ≡ p by (d) Therefore, (p ∧ ∼q) ∨ (p ∧ q) ≡ p. 6) Use…Let p and q be two propositions. Consider the following two statements in prepositional logic. S₁: (-p^(pv q)) → p S₂: q→(-p^ (pvq)) Which of them is tautology
- Question # 2 : Show that each of these conditional statements is a tautologyby using truth tables. a) (p∧q)→p b) p→(p ∨q) c) ¬p →(p →q) d) (p∧q)→(p →q)Determine whether these statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. p ꓥ t and pConsider the predicates Martian (x): x is a MartianisGreen(x): x is green Use equivalence laws of first-order logic to identify the expression that is logically equivalent to ∀x (Martian(x) ˄ isGreen(x)) Group of answer choices ∃x (Martian(x)) ˅ ∃x (isGreen(x)) ∃x (¬Martian(x)) ˄ ∃x (¬isGreen(x)) ∀x (Martian(x)) ˄ ∀x (isGreen(x)) ∀x (¬Martian(x)) ˄ ∀x (¬isGreen(x))