In logic and related fields such as mathematics and philosophy, "if and only if" is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional, and can be likened to the standard material conditional combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other, though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, P if and only if Q means that P is true whenever Q is true, and the only case in which P is true is if Q is also true, whereas in the case of P if Q, there could be other scenarios where P is true and Q is false.
The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of conjunction, disjunction, implication, equivalence, and negation. Some sources include other connectives, as in the table below.
Q, or q, is the seventeenth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is pronounced, most commonly spelled cue, but also kew, kue and que.
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks. That system was declassified in 1997.
An electric field is the physical field that surrounds electrically charged particles. Charged particles exert attractive forces on each other when their charges are opposite, and repulse each other when their charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. The electric field of a single charge describes their capacity to exert such forces on another charged object. These forces are described by Coulomb's law, which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Thus, we may informally say that the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker further away. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, Electromagnetism is one of the four fundamental interactions of nature.
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H, or in blackboard bold by Although multiplication of quaternions is noncommutative, it gives a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ. With multiple inputs, XOR is true if and only if the number of true inputs is odd.
Capacitance is the capability of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.
This gallery of sovereign state flags shows the national or state flags of sovereign states that appear on the list of sovereign states. For flags of other entities, please see gallery of flags of dependent territories. Each flag is depicted as if the flagpole is positioned on the left of the flag, except for those of Iran, Iraq and Saudi Arabia which are depicted with the hoist to the right.
Q is a popular music online magazine. Originally published in print in the UK from 1986 to 2020, it was inactive from 2020 until 2023. In 2023, Q was revived as an online publication. It was founded in 1986 by broadcast journalists Mark Ellen and David Hepworth, who were presenters of the BBC television music series The Old Grey Whistle Test. Q's final printed issue was published in July 2020, but began posting new articles to their website in 2023 before being fully relaunched in 2024.
Kamaal Ibn John Fareed, better known by his stage name Q-Tip, is an American rapper, record producer, singer, and DJ. Nicknamed the Abstract, he is noted for his innovative jazz-influenced style of hip hop production and his philosophical, esoteric and introspective lyrical themes. He embarked on his music career in the late 1980s, as an MC and main producer of the influential alternative hip hop group A Tribe Called Quest. In the mid-1990s, he co-founded the production team The Ummah, followed by the release of his gold-certified solo debut Amplified in 1999. In the following decade, he released the Grammy Award-nominated album The Renaissance (2008) and the experimental album Kamaal the Abstract (2009).
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix
B&Q Limited is a British multinational DIY and home improvement retailing company, with headquarters in Eastleigh, England. It is a wholly owned subsidiary of Kingfisher plc. It was founded in March 1969 by Richard Block and David Quayle.
QAnon is a far-right American political conspiracy theory and political movement which originated in 2017. QAnon centers on fabricated claims made by an anonymous individual or individuals known as "Q". Those claims have been relayed and developed by online communities and influencers. Their core belief is that a cabal of Satanic, cannibalistic child molesters are operating a global child sex trafficking ring which conspired against Donald Trump. QAnon has direct roots in Pizzagate, an Internet conspiracy theory that appeared one year earlier, but also incorporates elements of many other theories. QAnon has been described as a cult.
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. For example, is a rational number, as is every integer. The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface Q, or blackboard bold
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, Mécanique analytique.
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb. Coulomb's law was essential to the development of the theory of electromagnetism and maybe even its starting point, as it allowed meaningful discussions of the amount of electric charge in a particle.
Quincy Matthew Hanley, better known by his stage name Schoolboy Q, is an American rapper from South Los Angeles, California. Hanley released his debut mixtape, ScHoolboy Turned Hustla (2008) and its sequel, Gangsta & Soul (2009) the following year. After signing with the Carson-based record label Top Dawg Entertainment, Hanley released his debut studio album, Setbacks (2011) and its follow up, Habits & Contradictions (2012) both to positive reception; both also performed moderately on the Billboard 200 chart as digital exclusives.
