How to | Use Logical Operators

The Wolfram Language supports logical operators not only for programming, but for mathematical operations as well.

The infix operators and stand for conjunction (And) and disjunction (Or), while is the prefix operator for negation (Not). The next two inputs are equivalent:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

You can use symbols instead of True and False. BooleanConvert symbolically evaluates many logical expressions. We expect to be :

In[3]:=
Click for copyable input
Out[3]=

Use Resolve to find truth values of quantified logical statements:

In[4]:=
Click for copyable input
Out[4]=

You can also use the existential quantifier to check that :

In[5]:=
Click for copyable input
Out[5]=

The Wolfram Language also recognizes the logical operator Implies; you can use it to show :

In[6]:=
Click for copyable input
Out[6]=
    

Use SatisfiableQ to check if and satisfy :

In[1]:=
Click for copyable input
Out[1]=