# If P, then Q.

# If isotherms are concave towards the " north-east " direction ( 45 °), then adiabats are concave towards the " east north-east " ( 31 °).

# If adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively ( like altitude on a contour map ), then as the eye moves towards the axes ( towards the south-west ), it sees the density of isotherms stay constant, but it sees the density of adiabats grow.

# If morality is objective and absolute, God must exist.

# If the beat on the new record hits before the beat on the current record then the new record is too fast, reduce the pitch and manually slow the speed of the new record to bring the beats back in sync.

# If the beat on the new record hits after the beat on the current record then the new record is too slow, increase the pitch and manually increase the speed of the new record to bring the beats back in sync.

# It's Not Funny If I Have To Explain It — 2004 ; strips from 1997 to 2004, with more of Adams ' handwritten notes

# I Can't Remember If We're Cheap or Smart — 2012

# If equals are added to equals, then the wholes are equal.

# If equals are subtracted from equals, then the remainders are equal.

# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers ≤ N

# If the remainder is 2, swap 1 and 3 in odd list and move 5 to the end ( i. e. 3, 1, 7, 5 )

# If the remainder is 3, move 2 to the end of even list and 1, 3 to the end of odd list ( i. e. 4, 6, 8, 2-5, 7, 9, 1, 3 )

# If the design is symmetrical in an axis parallel to the flag pole, obverse and reverse will be identical despite the mirror-reversal, such as the Indian Flag or Canadian Flag

# If not, the obverse and reverse will present two variants of the same design, one with the hoist on the left ( usually considered the obverse side, see flag illustrations ), the other with the hoist on the right ( usually considered the reverse side of the flag ).

# If two straight lines in a plane are crossed by another straight line ( called the transversal ), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will intersect ( also called the parallel postulate ).

# Associativity: If a * b and b * c are defined, then ( a * b ) * c and a * ( b * c ) are defined and equal.

# Identity: If a * b is defined, then a * b * b < sup >− 1 </ sup >

# If it persists, " gather facts and seek help.

# If the noun is animate, natural gender tends to dictate grammatical gender.

# If the borrowed word happens to have a suffix that the borrowing language uses as a gender marker, the suffix tends to dictate gender.

# If the borrowed word rhymes with one or more native words, the latter tend to dictate gender.

# If a project's spending becomes too much for a committee to continue funding, it must take the issue to the Project Committee.

# Affordable premium: If the likelihood of an insured event is so high, or the cost of the event so large, that the resulting premium is large relative to the amount of protection offered, it is not likely that the insurance will be purchased, even if on offer.

# If the German Armed Forces ( Wehrmacht ) were not in a position to break the danger from the Eastern front, then Nazi Germany would fall to Bolshevism, and all of Europe would fall shortly afterward ;

# At the third stage there are physical and social consequences, i. e., hangovers, family problems, work problems, etc.

# if you could dramatically improve how we do that, you'd be boosting every effort on the planet to solve important problems — the sooner the better ; and

# Reversal or improvement of symptoms or problems when the glucose is restored to normal

The second generation Holden Commodore | Commodore ( Holden VN Commodore # Calais | VN Calais pictured ) overcame the previous generation's width problems.

# To achieve international co-operation in solving international problems of an economic, social, cultural, or humanitarian character, and in promoting and encouraging respect for human rights and for fundamental freedoms for all without distinction as to race, sex, language, or religion ; and

A List of knapsack problems # Multiple constraints | multiple constrained problem could consider both the weight and volume of the boxes.

# that the development of consciousness, in particular through the practice of the Transcendental Meditation and TM-Sidhi programs including Yogic Flying, can enhance society's ability to resolve problems

* List of unsolved problems in chemistry # Physical chemistry problems

# Reality and problem centered-they have a tendency to be concerned with " problems " in their surroundings.

BQP is contained in the complexity class # P ( or more precisely in the associated class of decision problems P < sup ># P </ sup >), which is a subclass of PSPACE.

In computational complexity theory, the complexity class # P ( pronounced " number P " or, sometimes " sharp P " or " hash P ") is the set of the counting problems associated with the decision problems in the set NP.

More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.

The corresponding # P problems ask " how many " rather than " are there any ".

One consequence of Toda's theorem is that a polynomial-time machine with a # P oracle ( P < sup ># P </ sup >) can solve all problems in PH, the entire polynomial hierarchy.

This is an indication of the extreme difficulty of solving # P-complete problems exactly.

Surprisingly, some # P problems that are believed to be difficult correspond to easy P problems.

Examples of # P-complete problems include:

It is surprising that some # P-complete problems correspond to easy P problems.

There are probabilistic algorithms that return good approximations to some # P-complete problems with high probability.

Many # P-complete problems have a fully polynomial-time randomized approximation scheme, or " FPRAS ," which, informally, will produce with high probability an approximation to an arbitrary degree of accuracy, in time that is polynomial with respect to both the size of the problem and the degree of accuracy required.