#### Answer

a. True. The integers correspond to certain of the points on a number line (the numbers that can be written without a fractional component), and the real numbers
correspond to all the points on the number line. The integers are a subset of the rational numbers. The rational numbers are a subset of the real numbers. Hence integers are a subset of the real numbers.
b. False. 0 is neither positive nor negative.
c. False. Let r = -2. The -r = -(-2) = 2 which is positive.
d. False. Consider the real number 2.2, which is not an integer.

#### Work Step by Step

Recall that for all, every, for any, for each, given any are ways to express the quantifier $\forall$ (for all). There exists, for some, for at least one are ways to express the quantifier $\exists$.