Answer by Karl for What is the weird correspondance between subset ⊂ and...
In the usual development of set theory, the expression $A\subseteq B$ is defined to mean $\forall x(x\in A\to x\in B)$.Similarly, $A\cup B$ denotes the set of all $x$ satisfying $x\in A\lor x\in B$,...
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The implication (if $P$ then $Q$) is true IFF the set of assignments (propositional, first order, whatever depending on the setting) which satisfy $P$ is a subset of the set of assignments which...
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Answer by ryang for What is the weird correspondance between subset ⊂ and...
using (p ⇒ q) ≡ (¬p∨q) yielded a weird Venn diagramOkay, this is the Venn diagram (here, white space signifies that no element is contained there) that you are referring to:This diagram says: If it...
View ArticleWhat is the weird correspondance between subset ⊂ and implication ⇒?
As i am learning mathematical logic , I noticed similarities between the concepts of logical connecters and set operators.Most of these made sense like how p ∧ q corresponds to P ∩ Q. Statement p ∧ q...
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