2. Let D-E-(-2,-10,1,2). write negations for each of the following statements and determine which is true,...
6. (4 marks) Write down the negation of each of the following statements. Then determine whether the statement or its negation is true, and explain why (a) x E R, y E R such that xy 5. (b) z, y E R+ such that V z E Z+, > z.
Problem 1 true in the following cases, and false otherwise: Determine whether each of the following is true or false: 10 Grades) that the universe for x and y is (1, 2, 3). Also, assume that Ptx, y) is a predicate that is (a) Vy3x (x ty A P(x, y)). (d) Vy (x 3 -> P(x, y)). (e) 3x 3y (yxP(x, y))
EXERCISES 6 Write and simplify the negation to the following le statements a) 3x<x2+1< 5 W . x>2 Vy<3 6) $9xty >3 .01.29 Izs1. (x-y< L da ih abzc ad bad c) 4x<1e y>2 acd d) a<b<ce bread 2 i) { x=1 Vy <3 e) x+1 <4 K x 2 <24 <3x+S Iz>y>x. f) ab. (cs d & cze) g) { x< 1 v { x=3 • lyce Tyzl
For each wff, find an interpretation in which it is true and one in which it is false. Please answer both a and c 8. For each wff, find an interpretation in which it is true and one in which it is false. a. ( x)[A(x)Л (Vy)B(x,y)] b. [(Vx)A(x) -> (Vx)B(x)]-(Vx)[A(a) >B(x) c. (3x)[P(x) V Q(x)] /\ (Vx)[P(x)- Q(x)] 8. For each wff, find an interpretation in which it is true and one in which it is false. a. (...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
4. Find counterexamples to show that the following statements are talne (a) Vreal numbers x, xxx (b) Assume the domain for both x and y is D = {1,2,3). VX Vy. x2 + y2 <12 5. Write the negations for each of the following statements: (a) V real numbers x, if x > 3, then x? > 9. (b) V integers a, b, and c, if a - b is even and b-c is even, then a - cis even.
Write true or false for each of the following statements. Provide justification for each answer—if true, give a brief explanation. If false, either provide a counterexample or contrast the statement with a similar true statement, explaining why the two cases differ. cos(x) with initial conditions (5 points) The linear second-order equation 2xy" + 3y' + xy = y(0) = 2, y'(0) = -1 has a unique solution on the real line.
7. Determine the truth value of the following statements. (a) Bx E Q, x2-2 = 0 (b) BxE Z,Vy e R, x +y = 1 (c) V e Z, Fy e R, x+y = 1 (d) 3x E Z,By e Z, x2 + y2 = 9
Module Outcome #3: Translate prose with quantified statements to symbolic and find the negation of quantified statements. (CO #1) Module outcome #3: Translate prose with quantified statements to symbolic negation of quantified statements. (CO #1) (a.) Negate the statement and simplify so that no quantifier or connective lies within the scope of a negation: (Bx)(y)-P(x.y) AQ(x, y)) (b.) Consider the domain of people working at field site Huppaloo, Let M(xx): x has access to mailbox y. Translate into predicate logic...
2. Write negations of the following statements: a. Jim is inside and tome is at the Pool. b. Jim is taller or Tom is shorter. c. If this program worked then the data is in order. d. For all integers n, If n is divisible by 15 then n is divisible by 3 and n is divisible by 5. e. There exist an integer n such that n is even and n' +3n-1 is odd. Page 1 of S