A Common Principle of Boolean Algebra: xy = y

Pencil Sketch of George Boole
Figure 1:  I am, at present reading Boole's Mathematical Analysis of Logic.

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:

xy = y

.

e.g. 1:

Let:

x = 1

.

Let:

y = 0

.

Hence:

xy = y

Or, in formal-logic notation:

xy = 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:

xy = 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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