Answer to Question #94847 in Discrete Mathematics for Amrit

Question

Express the negation of the following statements WITHOUT using the negation symbol:
a. ∀x(−2 < x <3)
b. ∀x(0 ≤ x <5)
c. ∃x(−4 ≤ x ≤1)
d. ∃x(−5 < x <−1)
e. ∀x∃y(x2 < y)

Answer 1

a) $\exists x(x \leq2 \lor x\geq3)$

b) $\exists x(x \lt 0 \lor x\geq 5)$

c) $\forall x(x \lt-4 \lor x\gt1)$

d) $\forall x(x \leq-5 \lor x\geq-1)$

e) $\exists x \forall y (x^2 \geq y)$