EXERCISES 6 Write and simplify the negation to the following le statements a) 3x<x2+1< 5 W...
16)write the negation of the following statements q: There exists a rational number x such that x2=2
2. Let D-E-(-2,-10,1,2). write negations for each of the following statements and determine which is true, the original or the negation. Vx e D,3y E E such that xy 2 y True: OriginalNesgation a. b. 3x E D such that Vy E E, x y True: Original Negation
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.
4. Simplify and state the restrictions. 2x+8 4x+16 a) 3x 6x2–5x+1 b) x2-4 Х x2-x-2 x2-3x 2x2 4 1 c) x2+3x+2 + 1 x2+4x+3 11x d)- x2+3x-28 X-4
Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vx ((-0(x)) + (-E(x))) is simplified, because the negation symbols are direct in front of the predicates O and E. However, Væ -(P(2) V E(x)) is not simplified.) (i) -(3x (P(x) 1 (E(x) + S(x)))) (ii) -(Vx (E(x) V (P(x) +-(Sy G(x, y))))) Write a sentence in predicate logic (using the same predicates as above) which is true...
Discrete Math
in the final answer) 6. Write the negation of the following statements (without using (a). Un e Z+, 3p EP, n3 <p < (n + 1)3. (b). Vce R+,3K EZ+, Vn e Z, n > K → n n+100 < c.
1. (2 points) Write a negation for the following statements: (a) If N is a nonagon, then N is a polygon. (b) If r is divisible by 56, then x is divisible by 7 and r is divisible by 8.
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
1. Evaluate the iterated integrals: x2+2x+y a. JR 3x+3y dA, R: 15x32,0 sys 1 (Hint: Simplify the integrand first.) b. S ey/*dA where R is the region in the xy-plane bounded between y = x2 and y = x over the interval 1sx52. c. So Sex Sx**2 x dydzdx
2. Find the derivative and simplify. y = (3x-4)2 (1-x²)6