- 逻辑学蕴涵命题中的「→」和数学中的「⇒」有什么区别和共同点？ - 知乎
命题逻辑中的"→"符号表示了一个命题。比如说p→q，代表的是"p为真时，q为真"这么一个命题。而这个命题可能是真的，也可能是假的。我们在给出命题"p→q"时，目的就是为了去判别命题的真假。（或者以此命题为依据来判别其他命题的真假）
- In Logic is ⇒, →, and ⊃ basically the same symbol?
I am not sure as I have a few truth tables to write down and both symbols have been used in the questions, the → in most of them and ⇒ in one of them which makes no sense to me, especially that I'm not very good at logic $\endgroup$ –
- Mathematical Notation - Arrow Sign - Mathematics Stack Exchange
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- What does the function f: x ↦ y mean? - Mathematics Stack Exchange
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- Prove this proposition is a tautology: [(p ∨ q) ∧ (p → r) ∧ (q → r)] → . . .
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- 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 first step shows: (p ∧ q) → (p ∨ q) ≡ ¬(p ∧ q) ∨ (p ∨ q) I've been reading my text book and looking at Equivalence Laws
- logic - Showing $((A→B)→A)→A$ and $A,B ⊢ ¬(A→¬B)$ using Deduction . . .
6) $\lnot (A → ¬B)$ --- from 3) and 5) by $\lnot$-introduction, discharging [a] Thus, steps 3) to 6) are nothing more than an Indirect Proof : assume the negation of the sought conclusion and derive a contradiction
- discrete mathematics - Prove or disprove (p→q)→r and p→(q→r) are . . .
I was able to show using a truth table that the two statements (p→q)→r and p→(q→r) are NOT equivalent, I need to now verify using equivalence laws, and I'm stuck Any guidance would be very appreciated Here's what I got so far; (p → q) → r ≡ (¬p ∨ q) → r -- By Logical equivalence involving conditional statements
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