TRUE OR FALSE ? Justify your answer.

Question

a. There exist real numbers a and b such (a+b)^2 = a^2 + b^2.

b. For any real number x, there exists a unique number -x such that x + (-x) = 0.

c. Any integer n is either odd or even.

d. Any real number x can be written as a fraction.

Write the statements from above using the logical quantifiers ∀ and ∃ .

Negate the statements from above (first question) using the logical quantifiers ∀ and ∃ .

Answer 1

(a) true: a=0 or b=0
∃ a,b ∊ R : (a+b)^2 = a^2+b^2
(b) true
(c) true
(d) false