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Propositional logic connectives like AND and OR have analogs or representations in set theory. For example, the logical connective AND is represented in set theory by intersection, an element of X AND Y is the element of the intersection of sets X and Y. And similarly, the logical connective of OR is represented in set theory by union, an element of X OR Y is the element of the union of sets X or Y.

So what is the set theoretical representation of material implication. When I googled "set theory of material implication", I did not get anything explicit. Maybe I'm not searching the right phrases. Anyway, is the set representation of implication simply the subset, an element is a member of a set X implied by Y if X is a subset of Y. Is this right, or am I missing something?

This is very important to me. I'd like to have a firm foundation for material implication in terms of set theory. Is this a well known concept? Are there any on-line references I can review and quote? Thanks.

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# Set theory representation of material implication

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