Negation with quantifiers

Question

Q. Write down the negations of the following statements:

a. Every news site reported on the Winter Olympics.

b. There is some real number which is larger than any integer.

c. For all nonzero real numbers x and y, if x > y, then y/x < 1.

Answer 1

(a) There is at least one news site that did not report on the Winter Olympics

(b) There is NOT a number that is larger than any integer...

(c) There exist non-zero real numbers x and y, such that if x>y then y/x > 1