Logical Conjunction - Properties

Properties

commutativity: yes

associativity: yes

distributivity: with various operations, especially with or

others

with exclusive or:

with material nonimplication:

with itself:

idempotency: yes

monotonicity: yes

truth-preserving: yes
When all inputs are true, the output is true.

falsehood-preserving: yes
When all inputs are false, the output is false.

Walsh spectrum: (1,-1,-1,1)

Nonlinearity: 1 (the function is bent)

If using binary values for true (1) and false (0), then logical conjunction works exactly like normal arithmetic multiplication.

Read more about this topic:  Logical Conjunction

Famous quotes containing the word properties:

    The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.
    John Locke (1632–1704)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)