To solve this instance of the decision problem we must determine whether there is a truth value ( TRUE or FALSE ) we can assign to each of the variables ( x < sub > 1 </ sub > through x < sub > 4 </ sub >) such that the entire expression is TRUE.

This is one of many possible assignments, with for instance, any set of assignments including x < sub > 1 </ sub > = TRUE being sufficient.

: sentence A is < u > X </ u > entails sentence A is not < u > Y </ u > Stated differently, if the proposition expressed by the sentence A is < u > X </ u > is TRUE, then the proposition expressed by the sentence A is not < u > Y </ u > is also TRUE .</ ref >

In several axiomatic derivations of logic, this is effectively resolved by showing that ( P ∨ ¬ P ) and its negation are constants, and simply defining TRUE as ( P ∨ ¬ P ) and FALSE as ¬( P ∨ ¬ P ), without taking a position as to the principle of bivalence or the law of excluded middle.

Unlike conventional logic gate diagrams in which inputs and outputs hold the binary values of TRUE ( 1 ) or FALSE ( 0 ), the gates in a fault tree output probabilities related to the set operations of Boolean logic.

* TRUE ( Temporal Reasoning Universal Elaboration ), a discrete and continuous time simulation software program for 2D, 3D and 4D modeling

When the Eiken Club was in grave danger ( Chiharu had been forced to fill a resigning form, and the club building destroyed ), it was Kirika's turn to save the day by stating the TRUE reason where exactly had the money for running the clubs had gone and why would Cho pay so much attention on the crushing of the Eiken Club.

Before he can go, though, Diablo asks Johnny if he wants to know his TRUE purpose, the real meaning of his life, but Johnny is so focused on the ugly inseam of his coat that he doesn't pay attention, and ends up disappearing before being told.

For instance, a digital variable could provide three control properties: TRUE, FALSE and UNKNOWN according to its possible boolean values.

In computer science, satisfiability ( often written in all capitals or abbreviated SAT ) is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE.

For example, the formula a AND b is satisfiable because one can find the values a = TRUE and b = TRUE, which make ( a AND b ) = TRUE.

The question is: given the expression, is there some assignment of TRUE and FALSE values to the variables that will make the entire expression true?

The definition of NP-easy uses a Turing reduction rather than a many-one reduction because the answers to problem Y are only TRUE or FALSE, but the answers to problem X can be more general.

« THE TRUE OR UNTRUE STORY OF CAHIER DU SOIR » ( 1991 – 1992 ) »-Luc Ferrari.

( This does not apply to ' genuine ' intentional bitwise operations-used for example instead of multiplication or division by powers of 2 or for TRUE / FALSE flags.

Bloomfield College boats the highly successful TRUE Program though it's Residential Education and Housing office.

The TRUE program is a programming model designed to bring elements of the classroom into the residence halls.

0 " is TRUE if the nth turn is L ; and is FALSE if the nth turn is R.

That is the view that “ Snow is white ” is TRUE if and only if P is TRUE in the LOT, where P means the same thing in LOT as “ Snow is white ” means in the natural language.

Contrary to what is written above it was a TRUE Arnolt Aston Martin.

C-41 Processing can not be done on TRUE black and white negatives.

If the code had a single IF statement containing a single condition there would be two paths through the code, one path where the IF statement is evaluated as TRUE and one path where the IF statement is evaluated as FALSE.

* 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.

As an example, the field of real numbers is not algebraically closed, because the polynomial equation x < sup > 2 </ sup > + 1 = 0 has no solution in real numbers, even though all its coefficients ( 1 and 0 ) are real.

Also, no finite field F is algebraically closed, because if a < sub > 1 </ sub >, a < sub > 2 </ sub >, …, a < sub > n </ sub > are the elements of F, then the polynomial ( x − a < sub > 1 </ sub >)( x − a < sub > 2 </ sub >) ··· ( x − a < sub > n </ sub >) + 1

Here, < sub > n </ sub > denotes the sample mean of the first n samples ( x < sub > 1 </ sub >, ..., x < sub > n </ sub >), s < sup > 2 </ sup >< sub > n </ sub > their sample variance, and σ < sup > 2 </ sup >< sub > n </ sub > their population variance.

: When comparing the above illustration to the below text, please note that the above x: y aspect ratio values are shown as vertical orientation rectangles to better demonstrate visual differences, whereas the aspect ratio values of the text below are written as rotated horizontal orientation rectangles ( e. g. compare 3: 4 vertical orientation illustration to 4: 3 horizontal orientation text ).

In more general sense, each column is treated as a polynomial over GF ( 2 < sup > 8 </ sup >) and is then multiplied modulo x < sup > 4 </ sup >+ 1 with a fixed polynomial c ( x ) = 0x03 · x < sup > 3 </ sup > + x < sup > 2 </ sup > + x + 0x02.

The Battle of Alexander at Issus | The Battle of Issus / Alexander, 1529, Wood, 158, 4 x 120, 3 cm Alte Pinakothek, Munich.

4. 4 x 4 x 3. 5 cm

Size: 5. 5 x 3. 1 x 2. 5 cm.

The slope field of F ( x ) = ( x < sup > 3 </ sup >/ 3 )-( x < sup > 2 </ sup >/ 2 )- x + c, showing three of the infinitely many solutions that can be produced by varying the Constant of integration | arbitrary constant C.

As the derivative of a constant is zero, x < sup > 2 </ sup > will have an infinite number of antiderivatives ; such as ( x < sup > 3 </ sup >/ 3 ) + 0, ( x < sup > 3 </ sup >/ 3 ) + 7, ( x < sup > 3 </ sup >/ 3 ) − 42, ( x < sup > 3 </ sup >/ 3 ) + 293 etc.

If L ′ is of finite height, or at least verifies the ascending chain condition ( all ascending sequences are ultimately stationary ), then such an x ′ may be obtained as the stationary limit of the ascending sequence x ′< sub > n </ sub > defined by induction as follows: x ′< sub > 0 </ sub >=⊥ ( the least element of L ′) and x ′< sub > n + 1 </ sub >= f ′( x ′< sub > n </ sub >).

In other cases, it is still possible to obtain such an x ′ through a widening operator ∇: for all x and y, x ∇ y should be greater or equal than both x and y, and for any sequence y ′< sub > n </ sub >, the sequence defined by x ′< sub > 0 </ sub >=⊥ and x ′< sub > n + 1 </ sub >= x ′< sub > n </ sub > ∇ y ′< sub > n </ sub > is ultimately stationary.

We can then take y ′< sub > n </ sub >= f ′( x ′< sub > n </ sub >).

While Ruffini and Abel established that the general quintic could not be solved, some particular quintics can be solved, such as ( x − 1 )< sup > 5 </ sup >= 0, and the precise criterion by which a given quintic or higher polynomial could be determined to be solvable or not was given by Évariste Galois, who showed that whether a polynomial was solvable or not was equivalent to whether or not the permutation group of its roots – in modern terms, its Galois group – had a certain structure – in modern terms, whether or not it was a solvable group.

This notation is used because we have the rule ( x < sup > a </ sup >)< sup > b </ sup >= x < sup > ab </ sup > ( giving a right action of G on itself ).

The composition of two inner automorphisms is again an inner automorphism ( as mentioned above: ( x < sup > a </ sup >)< sup > b </ sup >= x < sup > ab </ sup >, and with this operation, the collection of all inner automorphisms of G is itself a group, the inner automorphism group of G denoted Inn ( G ).

Just to check that this is indeed a point on the curve: y < sup > 2 </ sup >= 54514 = x < sup > 3 </ sup >+ 5x-5 ( mod 455839 ).

This has no eigenvalues, since if Rx = λx then by expanding this expression we see that x < sub > 1 </ sub >= 0, x < sub > 2 </ sub >= 0, etc.