Theorems Cheat Sheet

Question 1

De Morgan’s Laws (DML)

Answer 1

Let A and B be Statements. Then,
¬(A ∨ B) ≡ ¬A ∧ ¬B
and
¬(A ∧ B) ≡ ¬A ∨ ¬B

Question 2

Bounds by Divisibility (BBD)

Answer 2

Let a, b ∈ Z.
If a | b and b != 0,
then |a| ≤ |b|.

Question 3

Transitivity of Divisibility (TD)

Answer 3

Let a, b, c ∈ Z.
If a | b and b | c,
then a | c

Question 4

Divisibility of Integer Combinations (DIC)

Answer 4

Let a, b, c ∈ Z.
If a | b and a | c,
then for all x, y ∈ Z,
a | (bx + cy)