安裝中文字典英文字典辭典工具!
安裝中文字典英文字典辭典工具!
|
- 逻辑学蕴涵命题中的「→」和数学中的「⇒」有什么区别和共同点？
剩下的不想贴图了，自己去找 GTM 看。 那么有没有除了集合论和数理逻辑（如 GTM022）之外依旧频繁出现 \forall \exists 的教材呢？ 按照某人的说法，分析教材里面很喜欢的 \varepsilon-\delta 应该是一个很好的例子。 但是 比如说 025 Real and Abstract Analysis,
- Difference between implies and turnstile symbols (→ and ⊢)
So this would imply to me that → and ⊢ are equivalent, but it's idiomatic to use ⊢ for metamathematics, and → otherwise Or, more concretely: (A → B) → (C → D) is the same as (A → B) ⊢ (C → D), but the second option is considered more idiomatic readable as we differentiate the smaller connections from the larger ones
- logic - Natural Deduction Proof: A ↔ B |- (C → A) → (C → B . . .
At this point we can proceed with conditional introduction (→I) used twice to derive the desired goal Since there was some concern about the existence of the conditional introduction rule, see section 15 3 in the forallx text linked to below for a discussion of the conditional and the associated introduction and elimination rules
- logic - Given the premises p→q and ¬p→¬q, prove that p is logically . . .
Given the premises p→q and ¬p→¬q, prove that p is logically equivalent to q I understand why this works, but I do not know how to construct a complete formal proof
- logic - How can I prove that (p→q)∧ (p→r) ⇔ p→ (q∧r) - Mathematics . . .
How can I prove that (p→q)∧(p→r) compound statements and compound statement p→(q∧r) are logically equivalent? And can I use logical equivalences on this proof?
- How to prove that $ [ (p→q)∧ (q→r)]→ (p→r)$ is a tautology without . . .
For some basic information about writing mathematics at this site see, e g , basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to
- Propositional Logic: (p ∧ q) → r ⊢ (p → r) ∨ (q → r)
That looks good, but I would use idempotence to introduce the second $\vee r$ in line 4 and then use implication equivalence in line 5 (rather than the other way around )
- discrete mathematics - Proving (p → r) ∨ (q → r) ≡ (p ∧ q) → r . . .
For the ( (p ∧ q) → r) → ( (p → r) ∨ (q → r)) part: This one was the main point of confusion (and what my question is all about) Proving a implication with a disjunction as the consequent was something I was unsure how to do (and what I've seen many other people have asked too online unsure about)
|
|
|