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is For All V  is distributive on AND operator? ----1

is ‘’there exist’’  is distributive over OR operator?  ----2

I have example in which this is true , but is true in general?

so logically checking without using any property above four statements are correct.

But is 1 and 2 always correct?

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Posting links only sorry:

https://math.stackexchange.com/questions/1522141/distributive-property-of-quantifiers

https://cse.buffalo.edu/~rapaport/191/distqfroverandor.html

A statement for help:

The universal quantifier distributes over conjunction, but not disjunction, and the existential quantifier distributes over disjunction, but not conjunction.

Where Universal quantifier means "For all" and existential quantifier means "There Exists"

Rather than remembering them Understanding the statements according to the question  helps.

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