Since p ⇒ q and ~ q ⇒ ~ p are equivalent by the principle of transposition ( see law of excluded middle ), p ⇒ q is indirectly proved.

For example, the mode of limited transposition that Messiaen labelled " Mode 1 ", which is the whole tone scale, contains the notes C, D, E, F, G, A ; transposing this mode up a semitone produces C, D, F, G, A, B. Transposing this up another semitone produces D, E, F, G, A, C. Since transposing the mode up a whole tone produces the same set of notes, mode 1 has only 2 transpositions.

( D ) Since the shape of the drop conforms to the force field, it does not appreciably affect the distribution of forces in the fluid.

Since the time of Catherine II the ranks of Abbot and Archimandrite have been given as honorary titles in the Russian Church, and may be given to any monastic, even if he does not in fact serve as the superior of a monastery.

Since this process does not involve any heat transfer or work, the First Law of Thermodynamics then implies that the net internal energy change of the system is zero.

Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.

Since its introduction at games by the " Roar from 34 ", led by Wild Bill Hagy and others, in the late 1970s, it has been a tradition at Orioles games for fans to yell out the " Oh " in the line " Oh, say does that Star-Spangled Banner yet wave " in " The Star-Spangled Banner ".

Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra-ket notation.

Since the movie omits the religious and mythical elements of Dick's original novel ( e. g. empathy boxes and Wilbur Mercer ), it falls more strictly within the cyberpunk genre than the novel does.

Since it reflects spoken language, it does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not.

" Since he does not understand Chinese, Searle argues, we must infer that the computer does not understand Chinese either.

Since it does not think, it does not have a " mind " in anything like the normal sense of the word, according to Searle.

Since a witness called by the opposing party is presumed to be hostile, cross-examination does permit leading questions.

Since dextromethorphan is an optical isomer of the Schedule II opiate levomethorphan ( but does not act like an opiate ), an exemption was necessary to keep it a non-controlled substance.

Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.

Since E. histolytica does not form cysts in the absence of bacteria, E. invadens has become used as a model for encystation studies as it will form cysts under axenic growth conditions, which simplifies analysis.

Since E. histolytica does not form cysts in vitro in the absence of bacteria, it is not possible to study the differentiation process in detail in that species.

Since the underlying behaviour doesn't violate local causality, it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.

Since does not coincide with as a category, and similarly for, is distinguished from.

Since He owns everything, He does not need the actions of anyone.

Since LimeWire is free software, nothing prevents people from making additional forks of LimeWire, unaffected by the shut down, if they wished, as long as it does not use LimeWire trademarks.

This rule goes beyond that and says, " Since the firearm might fire, assume that it will and make sure no harm occurs when it does.

Since FIDE titles are for life, a GM or IM does not count for the purposes of this requirement if he had not had a GM or IM result in the five years prior to the tournament.

Since Java does not allow errors to be compared as logic elements, as under Icon, the lengthy syntax must be used instead.

Since water that flows through a cave eventually comes out in streams and rivers, any pollution may ultimately end up in someone's drinking water, and can even seriously affect the surface environment, as well.

Since such substances may affect a person's judgment even after consuming relatively small amounts, zero tolerance is advocated by gun safety teachers.

Since the coastal wetlands also support an economically important coastal fishery, the loss of wetlands will also negatively affect this industry.

Since the amount of physical capital affects MRP, and since financial capital flows can affect the amount of physical capital available, MRP and thus wages can be affected by financial capital flows within and between countries, and the degree of capital mobility within and between countries.

Since they were discovered in the mid-1960s, histone modifications have been predicted to affect transcription.

Since Brown and Lenneberg believed that the objective reality denoted by language was the same for speakers of all languages, they decided to test how different languages codified the same message differently and whether differences in codification could be proven to affect behavior.

Since tidal forces generate currents in conducting fluids in the Earth's interior, they in turn affect the Earth's magnetic field.

Since every packet is repeated on every other port, packet collisions affect the entire network, limiting its capacity.

Since its effects were temporary, he believed it could be given to high officials and in this way affect the course of important meetings, speeches etc.

Since the Great Salt Lake is a shallow lake with gently sloping shores around all edges except on the south side, small variations in the water level greatly affect the extent of the shoreline.

Since it is based on a well-studied distribution with special properties, the Rayleigh distribution lends itself to analysis, and the key features that affect the performance of a wireless network have analytic expressions.

Since the solar wind carries disturbances which affect the magnetosphere and ionosphere, IMP-8 demonstrated the utility of continuously monitoring the solar wind.

Since the base is set to 0 in all cases and the limit 4 GiB, the segmentation unit does not affect the addresses the program issues before they arrive at the paging unit.

Since technology can affect environmental impact in many different ways, the unit for T is often tailored for the situation I = PAT is being applied to.

Since the vessel is designed to contain an exact amount of electrolyte this loss will rapidly affect the capacity of the cell and its ability to receive and deliver current.

Since teachers can affect how students perceive the course materials, it has been found that teachers who showed enthusiasm towards the course materials and students can affect a positive learning experience towards the course materials.

Since the tail is operating in the flowfield of the wing, changes in the wing incidence cause changes in the downwash, but there is a delay for the change in wing flowfield to affect the tail lift, this is represented as a moment proportional to the rate of change of incidence:

Since the color of a pipe does not affect its function, the

Since changes to the logging code can affect other sections, it could introduce bugs in the operation of the program.

Since they do not directly affect the Circle of Willis, they are not dealt with here.

Since the Universal Translator presumably does not physically affect the process by which the user's vocal cords ( or alien equivalent ) forms audible speech ( i. e. the user is nonetheless speaking in his / her / its own language regardless of the listener's language ), the listener apparently hears only the speaker's translated words and not the alien language that the speaker is actually, physically articulating ; the unfamiliar oratory is therefore not only translated but somehow replaced.

Since the NHC had previously rounded incorrectly to keep storms in Category 4 in each unit of measure, the change does not affect the classification of storms from previous years.