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. | |
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| Not all of these numbers are unequal, so this gives False. | |
In[2]:=
3 2 3
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| You can mix < and . | |
In[3]:=
3 < 5 6
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| Since both of the quantities involved are numeric, Mathematica can determine that this is true. | |
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| Mathematica does not know whether this is true or false. | |
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| !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
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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. | |
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| Mathematica leaves this expression unchanged. | |
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(p || q) && !(r || s)
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| You can use LogicalExpand to expand out the terms. | |
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LogicalExpand[ % ]
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