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(158) As a contrapositive to this enunciation, the Feist Court refused to accede that the substantive usefulness of the work is sufficient to overcome this threshold bar.
2 [??] 3 (Proof by contrapositive: [logical not]3 [??] [logical not] 2.) Let n [greater than or equal to] 3 and i, j, k distinct indices so that i < j, [a.sub.jk] = 1 and [a.sub.ik] = 0.
The most they can usually achieve is to convince people who love logic but hate contrapositives. (5)
But consider the contrapositive of this conditional: namely, that if water flowed out the faucet while the main valve was closed, then water would not flow.
The antagonistic [[GAMMA].sub.F] game given in the article with functional elements, shows that in the process of the sides' contrapositive and in the game against the nature, for getting the certain aim, when the preference of the player changes in time and it is necessary to choose the time's starting moments, making decision is lead to using the strictly ranked criteria.
Many students find it challenging to formulate the contrapositive: The maximum cannot occur at a point where the graph of the constraint crosses the level curves transversally.
Principles of logic dictate that the contrapositive (negation and reversal) of a true statement is always true.
For example, establish by induction that courage is desirable and use deduction to then conclude that cowardice is undesirable (II 8, 113b30), or secure the contrapositive of an intended statement by induction, then use modus tollens to establish the intended claim (II 8, 113b17-25).
Likewise, the contrapositive, and only the contrapositive, is necessarily true.
Comparing the two group variances, it is clear that there is no heteroskedasticity when [p.sub.1] = [p.sub.2], but by the contrapositive, if there is heteroskedasticity, we must have [p.sub.1] [not equal to] [p.sub.2].
This is roughly the contrapositive of Groarke's thesis [D1] which Stove attributes to Hume (pp.
The equivalence between a statement and its contrapositive is so obvious for an expert that, usually, he does not need any explanation.