Let p be “It is cold” and let q be “It is raining”. Give a simple verbal sentence which describes each of the following statements: a) ~p b) p ∧ q c) p ∨ q
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Let p be “It is cold” and let q be “It is raining”. Give a simple verbal sentence which describes each of the following statements:
a) ~p
b) p ∧ q
c) p ∨ q
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- 6. Given, A = p A (p V q) and B = p v (p A q). State whether A = B or not. 7. Let P(x), Q(x), and R(x) be the statements. "x is a student," “x is smart," and "x is shy," respectively. Express each of these statements using quantifiers; logical connectives; and P(x), Q(x), and R(x), where the domain consists of all people. a. Some students are shy. b. All smart people are not shy.Note that for this question, you can in addition use ``land'' for the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬. Given the following three sentences:A) Every mathematician is married to an engineer.B) A bachelor is not married to anyone.C) If George is a mathematician, then he is not a bachelor. a) Convert A,B,C into three FOL sentences, whereMn(x): x is a mathematician.Er(x): x is an engineer.Md(x,y): x is married to y.Br(x): x is a bachelor.george: George is a constant. b) Show that A does-not-entail C. (Hint: Consider defining an interpretation I such that I models A, but does-not-model C.)c) Show that {A,B} entails C. (Hint: For a given interpretation I, consider two difference cases, the case where Mn(george) is true, and the case Mn(george) is false. For both cases, argue that it is always that I models C).d) Convert A,B, lnot C into a set of clausal forms, number your clauses. (Note that C is negated here!) e) Derive the empty clause from the set of clauses…Let D = {-1, -2, -3} and E = {−3, 1, 2, 3, 5}. Write negations for each of the following statements and determine if the given statement is true or its negation. Explain your answer. (i) V E D, ³y € E such that x + y = 0. (ii) ay € E such that vx € D, x + y ≥ 2. (iii) vy € E, 3x = D such that xy ≥ 0.
- 1. A set of premises and a conclusion are given. Use the valid argument forms learned in class to deduce the conclusion from the premises, giving a reason for each step. Assume all variables are statement variables. а. руд b. g → r С. рлs t d. ~r e. ~g → u AS f. .. tQ: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b 2); The following two statements are logically equivalent (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True FalseQ: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices A): b→(s∧¬v) B): b→(s→¬v) C): s∧(¬v→b) D): (s∧¬v)→b
- Mathematical Logic. First-order or predicate logic. Exercises on structures and models. Show that neither of the following statements is logically implied by the other two. (This is done by giving a structure in which the statement in question is false, while the other two are true). 1. ∀x ∀y ∀z (Pxy→Pyz→Pxz) 2. ∀x ∀y (Pxy→Pyx-x=y) 3. ∀x ∃y Pxy→∃y ∀x Pxy Please be as clear as possible. Show and explain all the steps. Thank you very much.Use prolog for the coding Using prolog write a predicate to guess a number interactively from 1 to 100 in at most 4 tries. Output can be obtained with predicates write(X) and nl, and input with predicate read(X) (integer input will be followed by a “.”). The secret number can be hardcoded.Let p, q, and r be the statementsp: The high temperature today is more than 70 degreesq: I am involved in a car accident todayr: I do not drink any alcohol today(a) Invent a compound statement that uses all three of the propositions p, q, and r as well as whatever logical connectives you choose.(b) Write an English sentence that corresponds to the statement youconstructed in (a).(c) Make a truth table for the statement you constructed in (a).
- Objective: The objective of this discussion is to be aware of the field of logic. Problem Statement: Consider the statement: "There is a person x who is a student in CSEN 5303 and has visited Mexico" Explain why the answer cannot be 3r (S(x)→ M(x)).A formal "interpretation" of a set of formulas in predicate logic does the following: Select one or more: a. assigns an extension to every predicate letter in the formulas b. assigns a truth value to every predicate letter in the formulas c. assigns a value to every variable in the formulas d. specifies a "domain of discourse" for the formulas e. assigns truth values to all the sentence letters in the formulasA proposition s is given. s: "2+9=15" The negation of the proposition s is "2+9=11" YES cannot be decided NO OTHER