Solution to What is the De Morgan’s law for quantifiers? (b) Write the negation of following statements. … - Sikademy
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Archangel Macsika

What is the De Morgan’s law for quantifiers? (b) Write the negation of following statements. (i) ∃x (x 2 + 2 < 1) (ii) ∀x (x - 2 ≥ 3) (iii) ∀x (x 2 ≥ 0 and x + 2 < 1) (iv) ∃x (x 2 + 2 < 0 or x - 5 ≥ 0) (v) ∀x (x - 2 ≥ 3 and x 3 + 5 ≤ 2) (vi) ∀x (x 2 = 2) (vii) There is a student in our class who likes chemistry. (viii) Every fox is cunning.

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a)

\neg \forall x P(x)\iff\exist x\neg P(x)

\neg \exist x P(x)\iff\forall x\neg P(x)


b)

i) \forall x (x^2+2\geq1)

ii) \exist x (x-2<3)

iii) \exist x (x^2<0 or x+2\geq1)

iv) \forall x (x^2+2\geq0 and x-5<0)

v) \exist x (x-2<3 or x^3+5>2)

vi) \exist x (x^2\not=2)

vii) All students in our class do not like chemistry.

viii) There exists a fox such that not cunning.

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