Relational and Logical Operators
| x==y | equal (also input as  ) |
| x!=y | unequal (also input as  ) |
| x>y | greater than |
| x>=y | greater than or equal to (also input as  ) |
| x<y | less than |
| x<=y | less than or equal to (also input as  ) |
| x==y==z | all equal |
| x!=y!=z | all unequal (distinct) |
| x>y>z, etc. | strictly decreasing, etc. |
Relational operators.
This tests whether
is less than
. The result is
False.
| Out[1]= |  |
Not all of these numbers are unequal, so this gives
False.
| Out[2]= |  |
You can mix
and
.
| Out[3]= |  |
Since both of the quantities involved are numeric,
Mathematica can determine that this is true.
| Out[4]= |  |
Mathematica does not know whether this is true or false.
| Out[5]= |  |
| !p | not (also input as  p) |
| p&&q&&... | and (also input as  ) |
| p||q||... | or (also input as  ) |
| Xor[p,q,...] | exclusive or (also input as  ) |
| 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.
| 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.
| Out[7]= |  |
Mathematica leaves this expression unchanged.
| Out[8]= |  |
| Out[9]= |  |
