This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Relational and Logical Operators

xyequal (also input as x = y)
xyunequal (also input as x y)
x>ygreater than
x>=ygreater than or equal to (also input as x y)
x<yless than
x<=yless than or equal to (also input as x y)
xyzall equal
xyzall unequal (distinct)
x>y>z, etc.strictly decreasing, etc.

Relational operators.

This tests whether 10 is less than 7. The result is False.
In[1]:=
Click for copyable input
Out[1]=
Not all of these numbers are unequal, so this gives False.
In[2]:=
Click for copyable input
Out[2]=
You can mix < and <=.
In[3]:=
Click for copyable input
Out[3]=
Since both of the quantities involved are numeric, Mathematica can determine that this is true.
In[4]:=
Click for copyable input
Out[4]=
Mathematica does not know whether this is true or false.
In[5]:=
Click for copyable input
Out[5]=
!pnot (also input as ¬p)
p&&q&&... and (also input as p q ... )
p||q||... or (also input as p q ... )
Xor[p,q,...]exclusive or (also input as p q ... )
Nand[p,q,...] and Nor[p,q,...]
nand and nor (also input as and )
If[p,then,else]give then if p is True, and else if p is False
LogicalExpand[expr]expand out logical expressions

Logical operations.

Both tests give True, so the result is True.
In[6]:=
Click for copyable input
Out[6]=
You should remember that the logical operations , && and || are all double characters in Mathematica. If you have used a programming language such as C, you will be familiar with this notation.
Mathematica does not know whether this is true or false.
In[7]:=
Click for copyable input
Out[7]=
Mathematica leaves this expression unchanged.
In[8]:=
Click for copyable input
Out[8]=
You can use LogicalExpand to expand out the terms.
In[9]:=
Click for copyable input
Out[9]=