3.7.21. Write the negation of the following statements without using the negation symbol . Also, for each statement, decide whether it is true or false. Explain your answer briefly. (a) (Vr E R)(3y E R)(x² > y²) (b) (3z € Z) [(2² = (x+ 1)*) = (2³ € Z)] ©2017 Shay Fuchs. All rights reserved. 79 3.7. EXERCISES FOR CHAPTER 3 CHAPTER 3. INFORMAL LOGIC (c) (Vn E N)[(n – 1)* + n° # (n + 1)*] (d) [( E R)(r > 0)) = [(Vx € R)(x = 1+1)| (e) (Vz € R)( (z² < -1) = [(x + 1)² = x? + 1]] (f) (V ER)(x > 0) = (3n e N)(n- r > 1)| (g) (Vz ER)(3y E R(r + y)² = a² + y²) (h) (3y E R)(Vx E R)(r+ yl a|+ lul) (i) (Vz E Q)(3n E N)(n zE Z) G) (Vz ER)(Vy ER) (((+y S 7) A (ry r)) = (x< 7)| 3.7.22. For each statement below, write it and its negation using the logic symbols. Make sure to simplify

Question 97

3. Let A = {x, y, {x, y}}. Is {x, y} CA ? a. b. Is (x, y} E A ? Is {y} C A ? C. d. Is {y} € A ? 4. VZ EQ? Prove Is

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a. Given b2 = a? + c? – 2acCosB i) Transpose to make B the subject ii) Calculate B in degrees, minutes, and seconds, given that a = 150m, b = 200m, and c = 261m. %3D b. Given P, + (v,)² + Z1 = P2 + (V2)² + Z1 2g 2g Transpose to make P, the subject i) pg pg ii) Transpose to make v2 the subject

28. Prove: If S is open and S = AU B where AN B = A n B = Ø, then A and B are оpen.

Exercise 1.2.5 (De Morgan's Laws). Let A and B be subsets of R. (a) If x = (An B), explain why x € AU Bc. This shows that (An B)c C AC U Bc.

Image viewer A is a 7x7 matrix with three eigenvalues. One eigenspace is three-dimensional, and one of the other eigenspaces is three dimensional then it is possible that A is not diagonalizable.

1) X. Y, 2 O, elsewheve a) tind k 6) Fint P(X 62,12222).

1. Match each of the following coefficients of determination with one of the diagrams below. a) 0 b) 0.5 c) 0.9 i) iv) DIN G Embed TREUNG loza Por sonvacsorE ii) d) 1 19 of 664