- notation - In Logic is ⇒, →, and ⊃ basically the same symbol . . .
As for ⇒ ⇒, this has been used as a sequent former in formal sequent calculi; but also seems often to be used (in some places, at any rate) as a metalinguistic symbol (i e not part of a formal object language, but as shorthand in mathematical English) to mean "logically entails" (so something stronger than the material conditional)
- Why is the selection of logical connectives {¬,∨,∧,⇒,⇔}, in set theory?
Is not exhaustive either, since there are actually 16 possible compound statements (and corresponding logical connectives) to choose from (Since {¬,∨,∧,⇒,⇔} is already redundant, why not throw in the other 11 connectives, some of which are VERY helpful like "nand" ⊼ , "nor" ⊽ and "exclusive or" ⊻?) Some of the "16 possible compound statements" are in fact trivial cases (and
- Implication and equivalence arrows, when to use them?
In my course book we have something called implication arrows ⇒ ⇒ and equivalence arrows ⇔ ⇔ and I have never managed to understand them When do I know which to use and how do I know that I'm correct when I use them?
- What is the difference between implication symbols:
16 There is no universally observed difference between the two symbols ⇒ ⇒ tends to be used more often in undergraduate instruction, where the logical symbols are used to explain and elucidate ordinary mathematical arguments -- for example, in real analysis
- What are these symbols in logic called? - Mathematics Stack Exchange
Sometimes yes; sometimes ⇒ ⇒ means logical consequence; sometimes ⇒ ⇒ means a meta-linguistic (= mathematical English) "if then" Is ↔ ↔ (a connective between formulas, to create a compound formula, defined in terms of → →) called (material) equivalence?
- Difference between implies and turnstile symbols (→ and ⊢)
According to Wikipedia's list of logic symbols: A → B means A → B is false when A is true and B is false but true otherwise A ⊢ B means x ⊢ y means x proves (syntactically entails) y But for me I
- Simplicify $((A ⇒ B) ⇒ (B ⇒ A)) ⇒( ¬(A∧B) ⇔ ¬(B∨A))$
Rather than defining ∧ ∧ by using , I would define using ∨ ∨, and get rid of all those arrows Once you have just ¬, ∧ ¬, ∧ and ∨ ∨, simplification is a bit easier than expressions containing only ¬ ¬ and , in my opinion Of course, you could just draw up a truth table; there would only be four rows, after all
- discrete mathematics - Show that (p ∧ q) → (p ∨ q) is a tautology . . .
I am having a little trouble understanding proofs without truth tables particularly when it comes to → Here is a problem I am confused with: Show that (p ∧ q) → (p ∨ q) is a tautology The firs
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