discrete mathematics - Show that (p ∧ q) → (p ∨ q) is a tautology ...
2016年3月7日 · So far we have shown that $ (P \to Q) ~\vdash (\neg P \lor Q)$. To finish proving the equivalency $ P \to Q \equiv \neg P \lor Q ~$ we also need to show $ (\neg P \lor Q) …
propositional calculus - Prove $p ↔ q$ and $(p ∧ q) ∨ (¬p ∧ ¬q)
2020年6月12日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
discrete mathematics - Is $[p \land (p \to q)] \to q$ a tautology ...
2016年1月14日 · Start with the given statement, $$ [p \land (p \rightarrow q)] \rightarrow q.$$ As you noticed, from the first logical equivalence in Table 7, you can replace the part in the round …
logic - Prove (¬P ∨ Q) ↔ (P → Q) - Philosophy Stack Exchange
2018年8月14日 · Prove ~P ˅ Q entails P → Q, by assuming P and demonstrating that eliminating the disjunction will derive Q by means of explosion (P,~P ├ Q) and reiteration (P, Q ├ Q). …
logic - Given the premises p→q and ¬p→¬q, prove that p is …
2020年1月19日 · 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. So far, …
How to prove the theorem (¬P ∨ ¬Q) ↔ ¬ (P ∧ Q)?
2020年10月16日 · And the idea is that I am trying to prove ~(P ^ Q) -> (~P v ~Q) so that I can use the biconditional rule to end up with (¬P ∨ ¬Q) ↔ ¬(P ∧ Q). However, I am stuck on this and I …
propositional calculus - Simplify, equivalent for (p ∨ ¬q) ∧ (¬p ∨ …
2019年6月15日 · (p ∨ ¬q) ∧ (¬p ∨ ¬q) Looking at an equivalency table I did, it seems p ∨ ¬q gives the same results as (p ∨ ¬q) ∧ (¬p ∨ ¬q). However I'm not sure how you would deduce this …
discrete mathematics - How can I simplify and verify the logical ...
2016年10月20日 · ∼(p ∨∼q) ∨ (∼p ^ ~ q) ≡ ~p. Please help I don't know where to start. These are the laws I need to list in each step when simplifying. Commutative laws: p ∧ q ≡ q ∧ p p ∨ q ≡ q …
The difference between "P if Q" and "P only if Q"?
2017年2月12日 · Once again, we see that 'P only if Q' has the same meaning as 'If P then Q'. And (once again) because we translate 'If P then Q' as 'P-→ Q', it follows that we translate 'P only if …
logic - How can I prove that (p→q)∧ (p→r) ⇔ p→ (q∧r)
2019年4月16日 · $(p→q)∧(p→r) $ is the same as $(\overline{p} \vee q)\wedge (\overline{p} \vee r)$ which is the same as $(\overline{p}\vee(\overline{p}\wedge …