A Common Principle of Boolean Algebra: xy = y

Statement of the Common Principle:

Should:

x = U

or, in other words:

x = 1

Then, in Boolean Notation :

xy = y

Or, in formal-logic notation:

x ∧ y = y

.

e.g. 1:

Let:

x = 1

.

Let:

y = 0

.

Hence:

xy = y

Or, in formal-logic notation:

x ∧ y = y

, because:

1 × 0 = 0

, or:

1(0) = 0

, or, in formal-logic notation:

1 ∧ 0 = 0

.

e.g. 2:

Let:

x = 1

.

Let:

y = 1

.

Hence:

xy = y

Or, in formal-logic notation:

x ∧ y = y

, because:

1 × 1 = 1

, or:

1(1) = 1

, or, in formal-logic notation:

1 ∧ 1 = 1

.

Addendum:

You may read George Boole's Mathematical Analysis of Logic, for free at Project Gutenberg