* If S and T are in M then so are S ∪ T and S ∩ T, and also a ( S ∪ T )

* If S and T are in M with S ⊆ T then T − S is in M and a ( T − S ) =

* If a set S is in M and S is congruent to T then T is also in M and a ( S )

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

* If M is some set and S denotes the set of all functions from M to M, then the operation of functional composition on S is associative:

If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

If ( m, n ) is regular and M and N have i and j prime factors respectively, then ( m, n ) is said to be of type ( i, j ).

If X is a set and M is a complete metric space, then the set B ( X, M ) of all bounded functions ƒ from X to M is a complete metric space.

If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.

If used, the word „ gothic “ was used to describe ( mostly early ) works of F. M. Dostoevsky.

If ψ is satisfiable in a structure M, then certainly so is φ and if ψ is refutable, then is provable, and then so is ¬ φ, thus φ is refutable.

If is satisfiable in a structure M, then, considering, we see that is satisfiable as well.

If the password is correct, then M releases the transferred sum to B ( 3b ), usually minus a small commission.

If M is an R module and is its ring of endomorphisms, then if and only if there is a unique idempotent e in E such that and.

If this new Bible does not increase in significance by repeated readings throughout the years, it will not survive the ages as has the King James Version.

If birds don't belong in a Square or Park, what does??

If private brand competition hasn't been felt in your product field as yet, have you thought how you will cope with it if and when it does appear??

If Af leads to an address Af that is equal to the address computed from Af, even though Af does not match Af, the chain of information cells is extended from Af by storing the address of the next available cell in the Y-region, Af, in Af.

If both George and a piece of information George does not have are prominent in the context, but the idea of telling George is new, then dominant stress will probably be on tell in why not tell George??

If, on the other hand, it is not settled, or while it is being debated and resolved, does the Federal government have a responsibility in situations like that in Prince Edward County??

If this threefold division of costs were to have its counterpart in the actual rates of charge for service, as it actually does have in some rates, there would result a three-part rate for any one class of service.

If this attitude is seriously questioned in the Soviet Union, it does not necessarily follow that the majority of the society in which I live is too aware of the necessity for clarity on this ethical as well as aesthetic point of view.

If a continuation card follows a statement that does not permit continuation cards, the compiler will generate a NOP and issue an error message.

If the compiler does encounter such statements, a warning message will be issued.

If the fourth dimension is a physical concept and not purely metaphysical, through what medium does it extend??

If a child does lose his first teeth prematurely because of decay -- and if no preventive steps are taken -- the other teeth may shift out of position, become overcrowded and malformed.

If he does, it's still better than an even chance he won't notice the transposition of the numbers, and if he should notice it, the thing can be passed off as an honest mistake.

If the administration does not succeed in passing the sales tax bill, or any other tax bill, it could very well be faced this spring at the fiscal session of the Legislature with an interesting dilemma.

If Bultmann's own definition of myth is strictly adhered to ( and it is interesting that this is almost never done by those who make such pronouncements ), the evidence is overwhelming that he does not at all exaggerate the extent to which the mythological concepts of traditional theology have become incredible and irrelevant.

If you know that he ( God ) is just ( righteous ), know that everyone also who does what is just ( righteous ) has been born of him.

If I get a low M. R., I do so because I want it that way or my dark self does.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

If the appellate court does find a legal defect in the decision " below " ( i. e., in the lower court ), it may " modify " the ruling to correct the defect, or it may nullify (" reverse " or " vacate ") the whole decision or any part of it.

If it does, ocean levels would rise by a few metres in a very short period of time.

If, however, there are no shares left when the chain is founded, then the founding player does not receive the free share.

If Anne formed an attachment to Weightman it does not imply that he was attracted to her.

If the numbering does not start at 0, the constant B may not be the address of any element.

If abiotic stress does not have a strong presence in an area, the biodiversity will be much higher.

If light moves instantaneously, the telescope does not move, and the true direction of the star relative to the observer can be found by following the line ES.

If they are Beach cops on a stake-out, they'll admit it to a reporter.

If we admit that ruff and trump are convertible terms, of which there is scarcely a doubt, the game of trump was the precursor of whist.

Proposals to admit Turkey have been debated but are now currently stalled, partly on the ground that Turkey is beyond Europe's historic frontier and it is yet to comply with the 35 point policy areas set out by the E. U. If all or most East European states become members, the frontier may be the boundaries with Russia and Turkey.

If this be a spirit of aggrandizement, the undersigned are prepared to admit, in that sense, its existence ; but they must deny that it affords the slightest proof of an intention not to respect the boundaries between them and European nations, or of a desire to encroach upon the territories of Great Britain.

If the defendant chooses to file an answer within the time permitted, the answer must address each of the plaintiffs ' allegations by admitting the allegation, denying it, or pleading a lack of sufficient information to admit or deny the allegation.

Stephen Thomas Erlewine of Allmusic gave the album a negative review, remarking that " If you do happen to enjoy their ridiculously stupid jokes, Oi to the World is nearly as fun as anything else in their catalog, even though you might admit their fast, goofy, and essentially tuneless songs are beginning to wear a bit thin.

If then they speak of persons without hypostasis they are talking nonsense, ex hypothesi ; but if they admit that the person exists in real hypostasis, as they do acknowledge, let them so number them as to preserve the principles of the homoousion in the unity of the godhead, and proclaim their reverent acknowledgment of Father, Son, and Holy Spirit, in the complete and perfect hypostasis of each person so named.

If this be a spirit of aggrandizement, the undersigned are prepared to admit, in that sense, its existence ; but they must deny that it affords the slightest proof of an intention not to respect the boundaries between them and European nations, or of a desire to encroach upon the territories of Great Britain.

If the Ming Dynasty was willing to give support and money that would be beneficial to the Qing's economy, the Qing Dynasty in exchange would not only be willing to not attack the borders, but also admit itself as a country one level lower than the Ming Dynasty ; however, since all the Ming Court officials were reminded of the Jin Empire during the Song Dynasty, the court heavily refused the exchange.

* If both and admit a differentiable structure, the subset

Krugman elaborated: " If you admit that life is unfair, and that there ’ s only so much you can do about that at the starting line, then you can try to ameliorate the consequences of that unfairness.

If the court feels evidence has been wrongly obtained, it can refuse to admit it ”.

If M does not admit a finite flat resolution, then by convention the flat dimension is said to be infinite.

If we admit that the concretization of ideals genuinely occurs, Royce argues, then we are not only entitled but compelled to take seriously and regard as real the larger intelligible structures within which those ideals exist, which is the purposive character of the divine Will.

" He also suggested that Harvard would not be facing this issue if other universities and colleges would admit Jews in similar numbers: " If every college in the country would take a limited proportion of Jews, I suspect we should go a long way toward eliminating race feeling among the students.

If defendants refused to " cooperate ", i. e., to admit guilt for their alleged and mostly fabricated crimes, they did not go on public trial, but suffered execution nonetheless.

If those changes unfavourably affect the college's status in the university, recognition can be withdrawn, which is to say the college would remain but it would no longer be able to admit students to the university.

If it were I would have to admit that I longer have friends named Ben Foster or Dan Schafer.

If it were otherwise, and the three persons were really one substance or thing ( una res ), we should be forced to admit that the Father and the Holy Spirit became incarnate along with the Son.

" You are instructed with the utmost diligence to proceed with the said fleet to sea and if the winds and weather will possibly admit of it to proceed directly for Chesapeake Bay in Virginia and when nearly arrived there you will send forward a small swift sailing vessel to gain intelligence .... If ... you find that they are not greatly superior to your own you are immediately to enter the said bay, search out and attack, take or destroy all the naval force of our enemies that you may find there.

If the masterpiece formerly, in the Bredel collection, called A Wooded Stream, honestly bears the date of 1650, or The Cottages under Trees of the Ford collection the date of 1652, the painter of these canvases cannot be Hobbema, whose birth took place in 1638, unless indeed we admit that Hobbema painted some of his finest works at the age of twelve or fourteen.

If the bishop rejects the clerk within that time he is liable to a duplex querela ( Latin ; " double complaint ": The procedure in ecclesiastical law for challenging a bishop's refusal to admit a presentee to a benefice ) in the ecclesiastical courts, or to a quare impedit in the common law courts, and the bishop must then certify the reasons of his refusal.

If the results are different between the two groups, it might be that women of one group are less likely to have had an abortion, or it might simply be that women of one group who have had abortions are less likely to admit to it.

# If you're wrong, admit it quickly and emphatically.