- 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
- 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
- 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
- elementary set theory - How to prove (A ⊆ B) ∧ (B ⊆ C) ⇒ (A ⊆ C . . .
How would I go about proving that, given A, B, C are sets; $[(A⊆B)∧(B⊆C)]⇒(A⊆C)$ Thanks for the help
- 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
- Show that (p ⇒ q) ⇒ (r ⇒ s) ⇐⇒ (p ⇒ r) ⇒ (q ⇒ s) is a tautology . . .
Show that $(p ⇒ q) ⇒ (r ⇒ s) ⇐⇒ (p ⇒ r) ⇒ (q ⇒ s)$ is a tautology? I am having a little trouble in proving this proofs without truth tables the idea for solve this question is to work out left
- In classical logic, why is - Mathematics Stack Exchange
Administrative note You may experience being directed here even though your question was actually about line 4 of the truth table instead In that case, see the companion question In classical logic, why is (p ⇒ q) (p ⇒ q) True if both p p and q q are False? And even if your original worry was about line 3, it might be useful to skim the other question anyway; many of the answers to
|