write each universally quantified statement symbolically. then state whether the statement is true or false. if the statement is false, provide a counter example.

a. For all natural numbers n, n ≥ 1
b. For all integers k, 1/k²+1 is not an integer
c. For all integers m and n, mn is an integer
d. For all real numbers x and y, (x+y)² = x² + y²
e. The product of two odd integers is an odd number
f. Every integer is a rational number
g. The reciprocal of a rational number is a rational number

use the terms like ∀, ∈, etc.