3. Determine the truth value of each of the following quantified statements. If a universally quantified statement is false, provide a counterexample. If an existentially quantified statement is true, provide an example. Otherwise, you don't need to justify. Y CDC3 (h) VxEZ (√x ≥1) (i) \x € R+ (x² + 3x) (j) 3x ER+ (1-3x > 7) (k) Vn E Z+ (4n is an even number) (1) Vn €Z+ (n5+ 3n² + 2 is an odd number) 17 (12. 4)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.6: Absolute Value Of Product In Open Sentences
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3. Determine the truth value of each of the following quantified statements. If a universally
quantified statement is false, provide a counterexample. If an existentially quantified
statement is true, provide an example. Otherwise, you don't need to justify.
Hx CR 3
(D) TY CRYS
(h) VxEZ (√x ≥ 1)
(i) Vx € R+ (x² + 3x)
(j) 3x ER+
(1 - 3x > 7)
(k) Vn € Z+ (4n is an even number)
(1) Vn € Z+ (n5 + 3n² + 2 is an odd number)
(m) 3y
(n) 3y
Z (y² = 4)
Z (y² # 4)
(0) Vy Z (y² + 4)
(p) 3x ((x € Z) ^ (0 < x < 1))
(q) Vx ((x ER) → (√XER))
(r) 3x ((x € Z) ^ (x < 5) ^ (x² > 10))
(s) Vx ((x € R+) → ((x > 0) v (x < 0)))
Transcribed Image Text:3. Determine the truth value of each of the following quantified statements. If a universally quantified statement is false, provide a counterexample. If an existentially quantified statement is true, provide an example. Otherwise, you don't need to justify. Hx CR 3 (D) TY CRYS (h) VxEZ (√x ≥ 1) (i) Vx € R+ (x² + 3x) (j) 3x ER+ (1 - 3x > 7) (k) Vn € Z+ (4n is an even number) (1) Vn € Z+ (n5 + 3n² + 2 is an odd number) (m) 3y (n) 3y Z (y² = 4) Z (y² # 4) (0) Vy Z (y² + 4) (p) 3x ((x € Z) ^ (0 < x < 1)) (q) Vx ((x ER) → (√XER)) (r) 3x ((x € Z) ^ (x < 5) ^ (x² > 10)) (s) Vx ((x € R+) → ((x > 0) v (x < 0)))
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