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1.5.6 Relational and Logical Operators


Relational operators.

  • This tests whether 10 is less than 7. The result is False.
  • In[1]:= 10 < 7

    Out[1]=

  • Not all of these numbers are unequal, so this gives False.
  • In[2]:= 3 != 2 != 3

    Out[2]=

  • You can mix < and <=.
  • In[3]:= 3 < 5 <= 6

    Out[3]=

  • Since both of the quantities involved are numeric, Mathematica can determine that this is true.
  • In[4]:= Pi^E < E^Pi

    Out[4]=

  • Mathematica does not know whether this is true or false.
  • In[5]:= x > y

    Out[5]=


    Logical operations.

  • Both tests give True, so the result is True.
  • In[6]:= 7 > 4 && 2 != 3

    Out[6]=

    You should remember that the logical operations ==, && and || are all double characters in Mathematica. If you have used the C programming language, you will recognize this notation as being the same as in C.

  • Mathematica does not know whether this is true or false.
  • In[7]:= p && q

    Out[7]=

  • Mathematica leaves this expression unchanged.
  • In[8]:= (p || q) && !(r || s)

    Out[8]=

  • You can use LogicalExpand to expand out the terms.
  • In[9]:= LogicalExpand[ % ]

    Out[9]=