Let the P(x, y) be the statement x = y + 1 and assume the domain consists of all real numbers (Explain it pls)
1. What is the truth value of ∃x∀yP(x, y)?
2. What is the truth value of ∀y∃xP(x, y)?
Let the domain for x and y be R, the set of real numbers. (a) Determine the truth value of ∀x∃y (y = √ x). Explain (b) Determine the truth value of ∃y∀x (y = √ x). Explain
2. Let Q(x,y) be the statement "x - 2 = 5y" and let the domain for x and y be all integers. Determine the truth value of each of the following statements. Justify your answers shortly. (i) Q(-3,-1) (ii) Vx3yQ(x,y) (iii) 3xVy-Q(x,y)
9. (5 points) Please translate this statement into English, where the domain for each variable consists of all real numbers. VrVyz(x = y + 2) 10. (5 points) Please determine the truth value of the staement Bruz Sy) if the domain for the variables consists of the nonzero real numbers. 11. (5 points) Please determine what rules of inference are used in this argument: "No man is an island. Manhattan is an island. Therefore, Manhattan is not a man." 12....
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
Suppose the domain of P(x, y) consists of pairs x and y, where x is 1, 2, or 3 and y is 1, 2, or 3. Express the statement ∃x∀y P(x, y) using disjunctions and conjunctions.
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.
3) Determine the truth value of each sentence. The domain of each variable consists of all real numbers (2 points) a) vxVy(x+y = y+x) (2 points) b) Vx3y-x-9 ) (2 points) c)x3y(8x-5y 3) (2 points) d)leV(x > 0 + (=logx)) (2 points) e) v i
3) Determine the truth value of each sentence. The domain of each variable consists of all real numbers (2 points) a) vxVy(x+y = y+x) (2 points) b) Vx3y-x-9 ) (2 points) c)x3y(8x-5y 3) (2 points)...
Let C(x,y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being given at your school. Express each of these statements by a simple English sentence. (20) + (2x)) (( # x))ZAEXE
QUESTION 9 Find the domain and range and describe the level curves for the function f(x,y) y+10 1(x, y)s a.Domain: all points in the x-y plane excluding x O: range: all real numbers; level curves: parabolas y ex2-10 b. Domain all points in the xey plane; range: real numbersz 0: level curves: parabolas y- ex2- 10 Domain :all points in the x-y plane; range: all real numbors; levol curvos: parabolas y ex2-10 d. Domain all points in the x-y plane...
Differential Geometry:
1) Give an example of two vector fields X,Y E X(R3) such that for almost all p ER3 the three tangent vectors Xp, Yp, [X,Y] are a basis, but for some p they are not. However, at those special points p the three tangent vectors Xp, Yp, [X, [X,Y]]p form a basis. (Hint: The fields X and Y may span the Martinet distribution.) 2) Prove that any pair of vector fields X,Y with property 1) cannot be tangent...