Mathematica logical function

It evaluates its arguments in order, giving False immediately if any of them are Falseand True if they are all True. Enter using and :. And works with any number of arguments:.

And is associative:. And with explicit True or False arguments will simplify:. And evaluates its arguments in order, stopping when an argument evaluates to False :. TraditionalForm formatting:. If an argument of And evaluates to Falseany subsequent arguments are not evaluated:. Combine equations and inequalities; And is used both in the input and in the output:. Use And to combine conditions:. A cellular automaton based on And :. Truth table for binary And :.

Ternary And :. Zero-argument And is True :. And with a single argument will return the evaluated argument regardless of value:. Use BooleanConvert to expand And with respect to Or :. De Morgan's laws relate AndOrand Not :. Conjunction of conditions corresponds to the product or Min of Boole functions:. Use Thread to thread over lists:. Introduced in 1. Wolfram Language. Wolfram Research. Last Modified Enable JavaScript to interact with content and submit forms on Wolfram websites.

Learn how. History Introduced in 1. APA Wolfram Language. Give Feedback Top.Joinsubscribers and get a daily digest of news, geek trivia, and our feature articles. By submitting your email, you agree to the Terms of Use and Privacy Policy. Logical functions are some of the most popular and useful in Excel. They can test values in other cells and perform actions dependent upon the result of the test. This helps us to automate tasks in our spreadsheets.

The IF function is the main logical function in Excel and is, therefore, the one to understand first. It will appear numerous times throughout this article. When performing the logical test with cell values, you need to be familiar with the comparison operators.

You can see a breakdown of these in the table below.

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In this example, we want to test if a cell is equal to a specific phrase. The IF function is not case-sensitive so does not take upper and lower case letters into account. In the formula below we test if cell B2 contains a number greater than or equal to The IF function is a lot more than just displaying different text on the result of a test. We can also use it to run different calculations. There are many ways of doing this.

And running different formulas dependent upon the values of other cells is a very powerful skill to have. In this third example, we use the IF function to track a list of due dates. But if the date is in the future, calculate the number of days until the due date. The formula below is used in column C. You may have heard of the term nested IFs before. This means that we can write an IF function within another IF function.

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We may want to do this if we have more than two actions to perform. We have now extended our formula to beyond what just one IF function can do. And you can nest more IF functions if necessary.

There are alternative formulas that can be cleaner than this nested IF approach. The IF function alone can only handle one condition, or comparison. These functions can test up to conditions, so are certainly not limited to just two conditions like is demonstrated here.

They are written the same. It is just their logic which is different. In addition to the OR function, there is also an exclusive OR function. This is called the XOR function. The XOR function was introduced with the Excel version. This function gets a little more confusing when more conditions are added. Then the XOR function returns:. In this example, sales are split over two halves of the year.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minute to sign up. Can I use BooleanTable? Sign up to join this community. The best answers are voted up and rise to the top. How to generate the truth table to prove logical equivalence?

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Related 4. Hot Network Questions. Question feed. Mathematica Stack Exchange works best with JavaScript enabled.This tutorial was made solely for the purpose of education and it was designed for students taking Applied Math It is primarily for students who have very little experience or have never used Mathematica and programming before and would like to learn more of the basics for this computer algebra system.

The Mathematica commands in this tutorial are all written in bold black fontwhile Mathematica output is in normal font. Finally, you can copy and paste all commands into your Mathematica notebook, change the parameters, and run them because the tutorial is under the terms of the GNU General Public License GPL.

You, as the user, are free to use the scripts for your needs to learn the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. The tutorial accompanies the textbook Applied Differential Equations.

As many other languages, Mathematica has several built-in logical operators.

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As you can see, the short-hand notation is the same as in C. The condition should in principle evaluate to True or False, in order for If to make a choice. If it evaluates to True, the first operator oper1 is evaluated, otherwise a second one. The second operator may be absent, in which case nothing is done for the False outcome Null is returned.

Since normally the arguments of the function are evaluated before the function itself, while in the case of If the operator which corresponds to True of False branch should only be evaluated after the condition is checked, we conclude that If uses non-standard evaluation. Operators Which and Switch These operators generalize If to situations where we have to switch between several possibilities.

Which is essentially a replacement for nested If statements. Switch in Mathematica resembles Switch in C, but differs from it significantly. First, it has a different extended in a sense functionality since it works on patterns patterns are extremely important.

We will cover them later.

mathematica logical function

Also, Break[] operator is unnecessary here, and so the fall-through behavior of C Switch is not possible patterns sort of compensate for this. Finally, in C Switch can be used in more sophisticated ways to put some entry points in the block of code -- this is not possible here.

Both Which and Switch are well-explained in Mathematica Help, and we refer to it for further details regarding them. These constructs are quite analogous to the ones in C, with the exception that the roles of comma and semicolon are interchanged with respect to C.

In general, loops are not very efficient in Mathematicaand in particular, the most effective in Mathematica functional style of programming does not involve loops at all. We will give just a few examples for completeness. In general, most Mathematica built-in functions do not introduce side effects, since they operate on a copy of the given expression. It is a good practice to localize all loop variables inside one of the scoping constructs available in Mathematica.

There are statements to realize local Goto within the loop -- Break[] and Continue[]. They work in the same way as they work in C. For example, here we will break from the Do loop after 4 iterations :. The parentheses in this example actually represent a composite operator, which is legitimate everywhere where the single operator is.

There are three scoping constructs used in Mathematica to localize variables -- ModuleBlock and With. Module does lexical scoping localizing names. Block does dynamic scoping localizing values. It turns out that programs that use loops are often inefficient in Mathematica. This makes the code cleaner and faster.

Let me illustrate this on a simple example. We will compute a sum of the first natural numbers.It evaluates its arguments in order, giving True immediately if any of them are Trueand False if they are all False. Combine assertions with :. Enter using or :. Or works with any number of arguments:. Or is associative:. Or with explicit True or False arguments will simplify:. Or evaluates its arguments in order, stopping when an argument evaluates to True :. TraditionalForm formatting:.

If an argument of Or evaluates to Trueany subsequent arguments are not evaluated:. Combine equations and inequalities; Or is used both in the input and the output:. Use to combine conditions:. A cellular automaton based on Or :.

Truth table for binary Or :. Zero-argument Or is False :. Or with a single argument will return the evaluated argument regardless of value:. Use BooleanConvert to expand And with respect to Or :. De Morgan's laws relate AndOrand Not :. Disjunction of conditions corresponds to the Max of Boole functions:.

mathematica logical function

Introduced in 1. Wolfram Language. Wolfram Research.

Last Modified Enable JavaScript to interact with content and submit forms on Wolfram websites. Learn how. Or [ e 1e 2… ] can be input in StandardForm and InputForm as.

Or has attribute HoldAlland explicitly controls the evaluation of its arguments.This tutorial was made solely for the purpose of education and it was designed for students taking Applied Math It is primarily for students who have very little experience or have never used Mathematica and programming before and would like to learn more of the basics for this computer algebra system.

The Mathematica commands in this tutorial are all written in bold black fontwhile Mathematica output is in normal font. Finally, you can copy and paste all commands into your Mathematica notebook, change the parameters, and run them because the tutorial is under the terms of the GNU General Public License GPL. You, as the user, are free to use the scripts for your needs to learn the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately.

The tutorial accompanies the textbook Applied Differential Equations. Since the Mathematica programming language called the Wolfram language is to a large extent a functional programming language, functions are the central objects here. The Wolfram Language has the most extensive collection of mathematical functions ever assembled. They can be accessed through the following web site:. A powerful tool of Mathematica is its ability to manipulate user-defined functions. This functions can be not only in terms of the internal build-in functions, but also in terms of procedures.

To define a function, just type in the formula. Function evaluation in Mathematica is indicated by square brackets. Ordinary parentheses are used exclusively for algebraic grouping.

mathematica logical function

To suppress output, type a semi-colon ; at the end of input of your command. However, in may cases, you may find it impossible to define the function's value in a single simple formula. Instead, you may need to carry out several steps of computation, using temporary variables. You may want several input values, and you may want the user to group some of those input values in curly brackets.

A function can also be defined analytically in another way. Say we want to define a cubic root function; then we type. The notion of a pure function comes from the calculus, and is widely used in functional programming languages, Mathematica in particular. From the practical viewpoint, the idea is that often we need some intermediate functions which we have to use just once, and we don't want to give them separate names.

Pure functions allow their use without assigning them names, storing them in the global rule base etc. Another application of them is that while they can be assigned to some symbols, they exist independently of their arguments and can be called just by name with the arguments being supplied separately, so that the "assembly" to the working function happens already at the place where the function is used.

Finally, these functions may be dynamically changed and modified during the program's execution.

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Wolfram language allows one to define a pure function in which arguments are specified as1, 2, etc. There are several equivalent ways to write pure functions in the Wolfram Language. The idea in all cases is to construct an object which, when supplied with appropriate arguments, computes a particular function. Thus, for example, if fun is a pure function, then fun[a] evaluates the function with argument a.It really was a perfectly planned trip. I like that the rental agency (Dollar Thrifty) includes a GPS.

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