discrete mathematics - Show that (p ∧ q) → (p ∨ q) is a tautology . . . 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 I know the answer to this but I don't understand the first step How is (p ∧ q)→ ≡ ¬(p ∧ q)? If someone could explain this I would be extremely
How to prove this is a tautology - Mathematics Stack Exchange $\begingroup$ Is somebody demanding a proof from you? If so, you need to tell us which particular formal proof system they want you to use -- there are many possible ones which are structured quite differently (even though they prove the same things), and a hint that works with one may well be useless for another system
How can I use a truth table to show that this is a tautology? To make a truth table, you make columns for all the variables and rows for all combinations of truth values of the variables Then you make as many columns as you want to assess the truth value of the statement in question If you want to prove something a tautology, it must be true for all values of the truth value of the variables
What is the best way check whether statement is tautology Yes, you can rework the logical expression just like you rework algebraic expressions If at the end you get TRUE FALSE (i e you get a value which does not depend on any variable), then the initial formula was a tautology or a contradiction E g you can rework any expression into Disjunctive Normal Form
How do you show that this is tautology? And what is tautology? $\begingroup$ In order for this to be a tautology, it has to be true for all possible values of the variables involved, in this case p and q A tautology is always true, it never gives you any information about the values of the variables involved $\endgroup$ –
What exactly does tautology mean? - Mathematics Stack Exchange To simplify, a tautology in plain English is stating the same thing twice but in a different manner So for example, the statement " this meaningless statement is non-meaningful " is a tautology, because it is essentially restating the same thing
What is the Conjunction Normal Form of a tautology? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers