# A Common Principle of Boolean Algebra as Stated in George Boole's 'Mathematical Analysis of Logic':

# 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

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