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4. Let the domain of x be the set of geometric figures in the plane, and...
please do A-C thank you 4. Let the universe of discourse, U, be the set of all people, and let M(x,y) be "x is the mother of y." Which of the following is a true statement? Translate it into English. a. (Ex)u((Vy)u(M(x, y))) b. (Vy)u((Ex)u(M(x, y))) C. Translate the following statement into logical notation using quantifiers and the proposition M(x, y) : "Everyone has a maternal grandmother."
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...
1. (5 pts.) True oR FALSE: (a) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v) F(u, v)dudv-F(u(x, y), v(x, y))drdy (b) Let R denote a plane region, and (u,v) (u(x,y),o(x,y)) be a different set of coordinates for the Cartesian plane. Then dudv (c) Let R denote a square of sidelength 2 defined by the inequalities r S1, ly...
Let F(x, y) be the statement "x can fool y" where the domain consists of all people in the world Use quantifiers to express each of these statements.
9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic 10. Give a logical expression with variables p, q, and r that's true only if p and q are false and r is true. 11. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qlx): x is a perfect square Are the following logical expressions propositions? If the answer is yes,...
Let B(x), W(x), and S(x) be the predicates B(x): x is a female W(x): x is a good athlete S(x): x is young Express each of the following English sentences in terms of B(x), W(x), S(x), quantifiers, and logical connectives. Assume the domain is the set of all people. a) All good athletes are not young. b) A person is a good athlete only if it is the case that both she is a female and she is young. c)...
4. (2 pts) The domain for the variables x, y are integers. Let us be given a propositional function with the following meaning 66 P(x, y) ' – X – x²y = -x2 – y”. Determine the truth value of the following expression. P(1, -1) True False
Let P(X) be the predicate " is a dragon." Let Q(x) be the predicate "x breathes fire.” Let R(x,y) be the predicate "x and y are the same object.” Let S be an arbitrary nonempty set. Rewrite the following English statements in symbolic no- tation using predicates P, Q, R, universal and existential quanti- fiers, and any variables you want. i. There are no dragons in S. ii. Not everything in S is a dragon. iii. There is at least...
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
true and false propositions with quantifiers. Answer the following questions in the space provided below. 1. For each proposition below, first determine its truth value, then negate the proposition and simplify (using De Morgan's laws) to eliminate all – symbols. All variables are from the domain of integers. (a) 3.0, x2 <. (b) Vr, ((x2 = 0) + (0 = 0)). (c) 3. Vy (2 > 0) (y >0 <y)). 2. Consider the predicates defined below. Take the domain to...