Properties
commutativity: yes
associativity: yes
distributivity: Biconditional doesn't distribute over any binary function (not even itself),
but logical disjunction (see there) distributes over biconditional.
idempotency: no
monotonicity: no
truth-preserving: yes
When all inputs are true, the output is true.
falsehood-preserving: no
When all inputs are false, the output is not false.
Walsh spectrum: (2,0,0,2)
Nonlinearity: 0 (the function is linear)
Read more about this topic: Logical Biconditional
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—Ralph Waldo Emerson (1803–1882)
“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)