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Are these statements true or false? The universe of discourse is ℕ. Explain how you determined your solution. ∀x(5 < x < 10 → ∃a∃b∃c(a2 + b2 + c2 = x)). ∃!x((x – 4)2 = 36). ∃!x((x – 11)2 = 49). ∃x∃y ( (x ≠ y) ∧ ((x – 4)2 = 36) ∧ ((y – 4)2 = 36) )

Are these statements true or false? The universe of discourse is ℕ. Explain how you determined your solution. ∀x(5 < x < 10 → ∃a∃b∃c(a2 + b2 + c2 = x)). ∃!x((x – 4)2 = 36). ∃!x((x – 11)2 = 49). ∃x∃y ( (x ≠ y) ∧ ((x – 4)2 = 36) ∧ ((y – 4)2 = 36) )

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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Are these statements true or false? The universe of discourse is ℕ. Explain how you determined your solution.

  1. ∀x(5 < x < 10 → ∃a∃b∃c(a2 + b2 + c2 = x)).
  2. ∃!x((x – 4)2 = 36).
  3. ∃!x((x – 11)2 = 49).
  4. ∃x∃y ( (x ≠ y) ∧ ((x – 4)2 = 36) ∧ ((y – 4)2 = 36) )

please type your answer. and can you please explain what the ! means when it is by the ∃.

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