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And (&&, 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.
  • And has attribute HoldAll, and explicitly controls the evaluation of its arguments. In e_1&&e_2&&..., the e_i are evaluated in order, stopping if any of them is found to be False.  »
  • And gives symbolic results when necessary, removing initial arguments that are True.  »
EXAMPLESCLOSE ALL
Basic Examples   (4)
Combine assertions with &&:
A symbolic conjunction:
A system of equations:
Enter using Esc and Esc:
Combine assertions with &&:
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A symbolic conjunction:
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A system of equations:
In[1]:=
Click for copyable input
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Enter using Esc and Esc:
In[1]:=
Click for copyable input
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 we reverse the last two arguments, 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   (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:
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