MATH 240 EXAM SCRIPT 2026 PRACTICE SOLUTION FULL QUESTIONS AND CORRECT ANSWERS GRADED A+

MATH 240 EXAM SCRIPT 2026 PRACTICE
SOLUTION FULL QUESTIONS AND CORRECT
ANSWERS GRADED A+



◍ An integer x is odd if.... Ans: there is an integer k such that
x=2k+1


◍ parity. Ans: whether a number is odd or even


◍ r is rational if.... Ans: there exist integers x and y such that y≠0 and
r=x/y where the greatest common divisor of both x and y is 1


◍ an integer x divides integer y iff.... Ans: x≠0 and y=kx for some
integer k


◍ integer n is prime iff.... Ans: n>1 and the only positive integers
that divide n are 1 and n


◍ an integer is composite iff.... Ans: n>1 and there is an integer such
that 1<m<n and m divides n


◍ An integer is either prime or.... Ans: composite


◍ non-negative. Ans: x ≥ 0

, ◍ non-positive. Ans: x <= 0


◍ Allowed assumptions in proofs. Ans: The rules of algebra
- ex: if x, y, and z are real numbers and x = y, then x+z = y+z


The set of integers is closed under addition, multiplication, and
subtraction
- In other words, sums, products, and differences of integers are also
integers


Every integer is either even or odd


If x is an integer, there is no integer between x and x+1


The relative order of any two real numbers
-ex: 1/2<1 or 4.2>3.7


The square of any real number is >= 0


◍ Things in lecture that can be used as assumptions. Ans: - the sum
of two rational numbers x and y is rational
- if n = ab, then a <= sqrt(n) or b <= sqrt(n)
- if a^2 is even, then a is even