Let x, y, and z be True statements, and a, b, and c be False statements. If (b V ~ y) → (n → a) = True, then n = True False Cannot be determined
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- Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample.Given a nonterminal A, which of the following statements is true about FIRST(A) and FOLLOW(A)? a.FIRST(A) can be a nonterminal b.FOLLOW(A) cannot be $ c.FOLLOW(A) can be ε d.FIRST(A) can be εConsidering p, r and q are statements, use logic laws to indicate: (pvq) →r ≡ (p→r) ᴧ (q→r) By using logic laws, determine if the statement below is a contradiction, tautology or neither. [p→(q→p)] ↔ (pᴧ¬p) By using logic laws, test if the argument below is valid: Either I exercise regularly, or I eat healthy. If I exercise regularly then I will not get fat. I got fat. Therefore, I am healthy.
- 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 ∨ qPart I. Let p, q, and r be the following simple statements: p: Sydney is the capital of Australia. q: Thirteen is a prime number. r: The Trinity University of Asia is in Quezon City. Express each of the following propositions as an English sentence and determine its truth value. Part II. Use the truth table to determine whether the following pairs of statement are logically equivalent or not . 1. ~(p↑q)and~p↑-q 2. p↓(q↑r)and(p↑q)↓(p↑r)Given four positive integers a, b, c, and d, compute the sum of those among them that are odd. Because you have not yet learned how to make decisions, use the fact that for a positive integer n, the expression n % 2 is either 0 or 1. (not allowed to use an if statement or conditonal)
- Let :P: Birds can fly.Q: 2+1=4.R: x is an integer.S: π is a rational number. CONSTRUCT THE SENTENCE OF THE FOLLOWING LOGICAL PROPOSITIONS. 1. ~ ((p ⊕ q) ↔ (~r)) →sThe equation of a line in standard form is ax + by = c , wherein both aand b cannot be zero, and a, b, and c are real numbers. If b≠0, then –a/b is the slope of the line. If a = 0, then it is a horizontal line, and if b = 0, then it is a vertical line. The slope of a vertical line is undefined. Two lines are parallel if they have the same slope or both are vertical lines. Two lines are perpendicular if either one of the lines is horizontal and the other is vertical or the product of their slopes is –1. Design the class lineType to store a line. To store a line, you need to store the values of a (coefficient of x), b (coefficient of y), and c. Your class must contain the following operations: If a line is nonvertical, then determine its slope. Determine if two lines are equal. (Two lines a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are equal if either a₁ = a₂, b₁ = b₂, and c₁ = c₂, or a₁ = ka₂, b₁ = kb₂ and c₁ = kc₂, and for some real number k.) Determine if two lines are parallel. Determine if…Let :P: Birds can fly.Q: 2+1=4.R: x is an integer.S: π is a rational number. CONSTRUCT THE SENTENCE OF THE FOLLOWING LOGICAL PROPOSITIONS. 1. ((p→q) ⊕ ~s) → q
- Given that A and B are real variables with values 1.5, and 2.5respectively, and C is integer variable with value 3, evaluate thefollowing: NOT(A<0) AND (B/C<=0).Let s be a string of length 2 with characters from {0, 1, 2}, and define statements a, b, c, and d as follows:a = “the first character of s is 0”b = “the first character of s is 1”c = “the second character of s is 1”d = “the second character of s is 2”. Describe the set of all strings for which each of the following is true.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…