Question

Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers.

  1. ∃x(x2=−1)∃x(x2=−1)

  2. ∃x∀y≠0(xy=1)∃x∀y≠0(xy=1)

  3. ∀x∃y(x2=y)∀x∃y(x2=y)

  4. ∃x∃y(x+y≠y+x)∃x∃y(x+y≠y+x)

  5. ∃x∀y(xy=0)∃x∀y(xy=0)

  6. ∀x∃y(x=y2)∀x∃y(x=y2)

  7. ∀x∀y∃z(z=x+y2)∀x∀y∃z(z=x+y2)

  8. ∀x≠0∃y(xy=1)∀x≠0∃y(xy=1)

  9. ∃x(x2=2)∃x(x2=2)

  10. ∀x∃y(x+y=1)∀x∃y(x+y=1)

  11. ∃x∃y((x+2y=2)∧(2x+4y=5))∃x∃y((x+2y=2)∧(2x+4y=5))

  12. ∀x∃y((x+y=2)∧(2x−y=1))

Answer 1