And

e1&&e2&&

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.

Details

  • And[e1,e2,] can be input in StandardForm and InputForm as e1e2. The character can be entered as &&, and, or \[And]. »
  • And has attribute HoldAll and explicitly controls the evaluation of its arguments. In e1&&e2&&, the ei 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 and:

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 Wolfram Language 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>0 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  (8)

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:

&& 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:

Introduced in 1988
 (1.0)
 |
Updated in 1996
 (3.0)