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The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". [9] [1] By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between P and Q is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q).
The proposition to be proved is P. We assume P to be false, i.e., we assume ¬P. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the law of noncontradiction. Since assuming P to be false leads to a contradiction, it is concluded that P is ...
10 −1 g dg decigram 10 1 g dag decagram 10 −2 g cg: centigram: 10 2 g hg hectogram 10 −3 g mg: milligram: 10 3 g kg: kilogram: 10 −6 g μg: microgram (mcg) 10 6 g Mg megagram 10 −9 g ng: nanogram: 10 9 g Gg gigagram 10 −12 g pg picogram 10 12 g Tg teragram 10 −15 g fg femtogram 10 15 g Pg petagram 10 −18 g ag attogram 10 18 g Eg ...
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However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...
Then the attraction force vector onto a sample mass can be expressed as: = Here is the frictionless, free-fall acceleration sustained by the sampling mass under the attraction of the gravitational source. It is a vector oriented toward the field source, of magnitude measured in acceleration units.
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The Summary. A patch of snow in Scotland known for lingering year-round has melted for the fourth consecutive year. It's just the 10th time in more than three centuries that it has vanished.