BUILT-IN MATHEMATICA SYMBOL

And

is the logical AND function. It evaluates its arguments in order, giving False immediately if any of them are False, and True if they are all True.

MORE INFORMATION

And can be input in StandardForm and InputForm as . The character can be entered as Esc && Esc, Esc and Esc or \[And]. »

And has attribute HoldAll, and explicitly controls the evaluation of its arguments. In , the are evaluated in order, stopping if any of them are found to be False. »

And gives symbolic results when necessary, removing initial arguments that are True. »

EXAMPLES

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Basic Examples (4)

Combine assertions with

:

A symbolic conjunction:

A system of equations:

Enter using Esc and Esc:

Combine assertions with

:

In[1]:=

Out[1]=

A symbolic conjunction:

In[1]:=

Out[1]=

A system of equations:

In[1]:=

Out[1]=

Enter using Esc and Esc:

In[1]:=

Out[1]=

Scope (5)

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:

The order of arguments may be important:

Symbolic transformations will not preserve argument ordering:

TraditionalForm formatting:

Applications (6)

Combine conditions in Mathematica code:

If an argument of And evaluates to False, any subsequent arguments are not evaluated:

The argument order in And matters; if the last two arguments are reversed, I

is evaluated:

Combine assumptions:

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:

Find the area of the intersection of sets given by algebraic conditions:

This shows the set:

Properties & Relations (6)

Truth table for And:

has higher precedence than

:

Use BooleanConvert to expand And with respect to Or:

De Morgan's laws relate And, Or, and Not:

Conjunction of conditions corresponds to the product or Min of Boole functions:

Use Thread to thread over lists: