SQL keyword ANY and ALL

Question

Hi Guys,

In SQL, 

<condition> ALL  evaluates to TRUE if inner query returns no tuples. { X < ALL (empty) == TRUE }

<condition> ANY evaluates to FALSE if inner query returns no tuples. { X < ANY (empty) == FALSE }

But what is the logical reason behind this ?

PS:

ping @Krish__,  @Anu007,  @Ashwin Kulkarni @reena_kandari  and @srestha ji.

Comments

If i say "My marks should be greater than all gate aspirants" . but there is no one who gave exam..then by default you are a topper and condition is true.
But If I say "my marks should be greater than any of the gate aspirant" but there is no one who gave exam. then condition is not true bcz there is nothing for comparison.
I think this should be reason.

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https://gateoverflow.in/1259/gate2007-61

https://gateoverflow.in/43313/gate2012-51

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May be that happens due to "implication" 

In case of "for all x" ,

it can be read like : " if such x exists then ..." 

but if no "X" exists even then statement is true as per implication rule.

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Wow!!!great example

Answer 1

Assume that you are given "For every x∈S, property P(x) holds". You can say that the statement is false only if you can produce an element x such that the property is not satisfied. But, there exists no such x to claim that. Hence "ALL  evaluates to TRUE if inner query returns no tuples".

Now similarly you are given "There exists x∈S such that property P(x) holds". Now this statement can only be asserted to be true when you can pick up an element x to show that this property is indeed satisfied. But since there is no such element "ANY evaluates to FALSE if inner query returns no tuples".

Comments

For a funnier reasoning: https://math.stackexchange.com/a/202466/261610