## 1.5.6 Relational and Logical Operators

 x y equal (also input as x y) x y unequal (also input as x y) x > y greater than x y greater than or equal to (also input as x y) x < y less than x y less than or equal to (also input as x y) x y z all equal x y z all 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]:=  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]=

 !p not (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]:=  7 > 4 && 2 3
 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]:=  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]=

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