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EquationsSolving Equations

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]=

EquationsSolving Equations