In propositional logic, biconditional introduction is a valid rule of inference.

Biconditional introduction is the converse of biconditional elimination.

In logic and related fields such as mathematics and philosophy, if and only if ( shortened iff ) is a biconditional logical connective between statements.

Likewise, for any propositions and, is a proposition, and similarly for disjunction, conditional, and biconditional.

In everyday discourse, however, such cases are rare, typically only occurring when the " if-then " premise is actually an " if and only if " claim ( i. e., a biconditional / equality ).

In logic and mathematics, the logical biconditional ( sometimes known as the material biconditional ) is the logical connective of two statements asserting " p if and only if q ", where q is a hypothesis ( or antecedent ) and p is a conclusion ( or consequent ).

In that case, in the conditional, the result is true, yet in the biconditional the result is false.

A common way of demonstrating a biconditional is to use its equivalence to the conjunction of two converse conditionals, demonstrating these separately.

When both members of the biconditional are propositions, it can be separated into two conditionals, of which one is called a theorem and the other its reciprocal.

Logical equality ( also known as biconditional ) is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.

If a formula begins with an atomic formula followed by the biconditional, the subformula to the right of the biconditional is a definition of the atomic formula, whose variables are unbound.

The symbol for the biconditional ("↔") signifies the relationship between the propositions is both necessary and sufficient, and is verbalized as " if and only if ", or, according to the example " If P then Q ' if and only if ' if not Q then not P ".

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

The connective system, or network, is tailored to meet the requirements of the objective, and it is therefore not surprising that a military body acting as a single coordinated unit has a different communication network than a factory, a college, or a rural village.

For example the standard glutamic acid ( glutamate ) and the non-standard gamma-amino acid gamma-amino-butyric acid ( GABA ) are respectively the brain's main excitatory and inhibitory neurotransmitters, hydroxyproline-a major component of the connective tissue collagen-is synthesised from proline, the standard amino acid glycine is used to synthesise porphyrins used in red blood cells, and the non-standard carnitine is used in lipid transport.

These modifications are often essential for the function or regulation of a protein ; for example, the carboxylation of glutamate allows for better binding of calcium cations, and the hydroxylation of proline is critical for maintaining connective tissues.

It is through the most active of these connective routes, the Turkish Straits, that the Black Sea joins the world ocean.

In terms of anatomy and histology, blood is considered a specialized form of connective tissue, given its origin in the bones and the presence of potential molecular fibers in the form of fibrinogen.

Bone tissue is a type of dense connective tissue.

Intramembranous ossification mainly occurs during formation of the flat bones of the skull but also the mandible, maxilla, and clavicles ; the bone is formed from connective tissue such as mesenchyme tissue rather than from cartilage.

In a TRAM procedure, a portion of the abdomen tissue group, including skin, adipose tissues, minor muscles and connective tissues, is taken from the patient's abdomen and transplanted onto the breast site.

In addition to the milk glands, the breast also is composed of connective tissues ( collagen, elastin ), white fat, and the suspensory Cooper's ligaments.

The inframammary fold, where the lower portion of the breast meets the chest, is an anatomic feature created by the adherence of the breast skin and the underlying connective tissues of the chest ; the IMF is the lower-most extent of the anatomic breast.

Collagen () is a group of naturally occurring proteins found in animals, especially in the flesh and connective tissues of vertebrates.

It is the main component of connective tissue, and is the most abundant protein in mammals, making up about 25 % to 35 % of the whole-body protein content.

Paradoxically, achieving this connective human quality has also moved his buildings away from the abstract imageability valued in contemporary architecture, and this is one reason why his buildings are under-appreciated at present.

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true.

Gelatin is a mixture of peptides and proteins produced by partial hydrolysis of collagen extracted from the skin, boiled crushed horn, hoof and bones, connective tissues, organs and some intestines of animals such as domesticated cattle, chicken, horses, and pigs.

In some vertebrates, haematopoiesis can occur wherever there is a loose stroma of connective tissue and slow blood supply, such as the gut, spleen, kidney or ovaries.

It is controversial whether the connective thus defined is properly rendered by the English " if and only if ", with its pre-existing meaning.

`` That is, if we can be sure this is Colcord's money '' --

The true artist is like one of those scientists who, from a single bone can reconstruct an animal's entire body.

It is nothing you can put your fingers on but the air suddenly fills with a high charge of electricity.

It is Eromonga -- look hard, you can see with your naked eye the wooden scaffolding on the cliff ''.

`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.

Accidental war is so sensitive a subject that most of the people who could become directly involved in one are told just enough so they can perform their portions of incredibly complex tasks.

The box is internally wired so the door can never be opened without setting off a screeching klaxon ( `` It's real obnoxious '' ).

The stink is all the same to me, but I really think they can make one another out blindfolded ''.

It is well then that in this hour both of `` national peril '' and of `` national opportunity '' we can take counsel with the men who made the nation.

but they can hardly deny that, exaggerated or not, the old panorama is dead.

As his disciples boast, even though his emphasis is elsewhere, Faulkner does show his awareness of the changing order of the South quite keenly, as can be proven by a quick recalling of his Sartoris and Snopes families.

An order can be chanced rather than chosen, and this approach produces an experience that is `` free and discovered rather than bound and remembered ''.

That, I thought, is at least one thing I can find out when we meet.

It is not a mess you can make sense of ''.

One can only speak of what is in front of him, and that now is simply the mess ''.

indeed, it is maintained that the sexual element in jazz, by freeing the listener of his inhibitions, can have therapeutic value.

What they discuss with dialectical seriousness is the degree to which sex can inspire the Muse.

The professed mission of this disaffiliated generation is to find a new way of life which they can express in poetry and fiction, but what they produce is unfortunately disordered, nourished solely on the hysteria of negation.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.