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)(r² > y²) (b) (3r e Z) [(z? = (x+ 1)²) = (r³ € Z)] ©2017 Shay Fuchs. All rights reserved. 79 3.7. EXERCISES FOR CHAPTER 3 CHAPTER 3. INFORMAL LOGIC (c) (Vn € N)[(n – 1)³ +n° ± (n+1)*] (d) [(Vz € R)(x > 0)] = [(Vr € R)(r = r+1)]| (e) (Vz E R)[ (r² < -1) → (r+1)² = r² + 1]] (f) (V E R)[(x > 0) = (In € N)(n- x > 1)] (g) (Vz E R)(3y E R)[(x+ y)² = x² + y²] (h) (3y E R)(Vr E R)(r + y| = |+lvl) (i) (V E Q)(3n E N)(n rE Z) G) (Vz E R)(Vy ER) [((r+y <7) A (ry= )) (r<7)] statement below, write it and its negation using the logic symbols. Make sure to simplify
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)(r² > y²) (b) (3r e Z) [(z? = (x+ 1)²) = (r³ € Z)] ©2017 Shay Fuchs. All rights reserved. 79 3.7. EXERCISES FOR CHAPTER 3 CHAPTER 3. INFORMAL LOGIC (c) (Vn € N)[(n – 1)³ +n° ± (n+1)*] (d) [(Vz € R)(x > 0)] = [(Vr € R)(r = r+1)]| (e) (Vz E R)[ (r² < -1) → (r+1)² = r² + 1]] (f) (V E R)[(x > 0) = (In € N)(n- x > 1)] (g) (Vz E R)(3y E R)[(x+ y)² = x² + y²] (h) (3y E R)(Vr E R)(r + y| = |+lvl) (i) (V E Q)(3n E N)(n rE Z) G) (Vz E R)(Vy ER) [((r+y <7) A (ry= )) (r<7)] statement below, write it and its negation using the logic symbols. Make sure to simplify
ChapterP: Prerequisites
SectionP.1: Review Of Real Numbers And Their Properties
Problem 13ECP: Identify the rule of algebra illustrated by the statement. a. x+9=9+x b. 5x32=5x32 c....
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B)e)j)
Prove the original statement if true or false
![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)(r² > y²)
(b) (3r E Z) [(z = (x + 1)²) = (r³ € Z)]
©2017 Shay Fuchs. All rights reserved.
79
CHAPTER 3. INFORMAL LOGIC
3.7. EXERCISES FOR CHAPTER 3
(c) (Vn € N)[(n – 1)' +n° ± (n+ 1)*]
(d) [(Vx € R)(x > 0)] = (Vr € R)(r = r+1)|
(e) (Vr E R)[ (r² < -1) → (x +1)? = ² + 1]]
(f) (VI € R)[(x > 0) → (3n € N)(n- x > 1)|
(g) (Vr € R)(3y € R)(r + y)² = x² + y²]
(h) (3y E R)(Vr E R)(r + y| = ||+ lyl)
(i) (Vr E Q)(3n E N)(n r E Z)
G) (Vz ER)(Vy ER) ((r+y S 7)^ (ay =)) (r<7)]
3.7.22. For each statement below, write it and its negation using the logic symbols. Make sure to simplify](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb149039b-c609-4874-85d1-64f29a0551b7%2Fb31b33f3-1d69-4706-8459-98de58831aeb%2F5jmowlj_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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)(r² > y²)
(b) (3r E Z) [(z = (x + 1)²) = (r³ € Z)]
©2017 Shay Fuchs. All rights reserved.
79
CHAPTER 3. INFORMAL LOGIC
3.7. EXERCISES FOR CHAPTER 3
(c) (Vn € N)[(n – 1)' +n° ± (n+ 1)*]
(d) [(Vx € R)(x > 0)] = (Vr € R)(r = r+1)|
(e) (Vr E R)[ (r² < -1) → (x +1)? = ² + 1]]
(f) (VI € R)[(x > 0) → (3n € N)(n- x > 1)|
(g) (Vr € R)(3y € R)(r + y)² = x² + y²]
(h) (3y E R)(Vr E R)(r + y| = ||+ lyl)
(i) (Vr E Q)(3n E N)(n r E Z)
G) (Vz ER)(Vy ER) ((r+y S 7)^ (ay =)) (r<7)]
3.7.22. For each statement below, write it and its negation using the logic symbols. Make sure to simplify
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