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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. 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)

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)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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