∧ = and

∨ = or

¬ = not

⇒ = if…then

⟺ = if and only if

Closure

a + b ∈ ℝ

Commutative

a + b = b + a

Associative

(a + b) + c = a + (b + c)

Distributive

a(b + c) = ab + ac

Additive Identity

a + 0 = a

Multiplicative Identity

a × 1 = a

Additive Inverse

a + (-a) = 0

Multiplicative Inverse

a × 1/a = 1 (a ≠ 0)

Universal (∀): For all

Existential (∃): There exists

Original: If P, then Q

Converse: If Q, then P

Inverse: If not P, then not Q

Contrapositive: If not Q, then not P

Types of Patterns:

Fractals: Self-similar geometric shapes with fractional dimensions.

Symmetry:

Bilateral: Mirror image (left-right symmetry)

Radial: Symmetry around a central point

Spiral: Curving shapes seen in shells, galaxies, flowers, etc.