|x==y||equal (also input as xy)|
|x!=y||unequal (also input as x≠y)|
|x>=y||greater than or equal to (also input as x≥y)|
|x<=y||less than or equal to (also input as x≤y)|
|x!=y!=z||all unequal (distinct)|
|x>y>z, etc.||strictly decreasing, etc.|
This tests whether 10 is less than 7. The result is False.
Not all of these numbers are unequal, so this gives False.
Since both of the quantities involved are numeric, the Wolfram Language can determine that this is true.
|!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|
You should remember that the logical operations ==, &&, and || are all double characters in the Wolfram Language. If you have used a programming language such as C, you will be familiar with this notation.
You can use LogicalExpand to expand out the terms.