Nov 11, 2025 · 2 It is a material conditional, or otherwise known as $p$ implies $q$, or if $p$, then $q$ The truth table for that is as follows p q p implies q T T T T F F F T T F F T $\rightarrow$ can also be …

Dec 20, 2020 · 0 $ (p,q)$ a common notation for $\gcd (p,q)$ and so $ (p,q)=1$ means that the fraction is irreducible.

Mar 7, 2016 · 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...

May 12, 2024 · From that perspective I have a hard time seeing how p -> q means the same thing as p only if q, especially when drawing out the truth table for it. I'm not sure if this is a language issue or …

Feb 5, 2021 · I'm new to the whole discrete math thing, and I'm having trouble finding any laws to start breaking the statement $p \land (\sim q \lor p) \equiv p$ down into its equivalences laws.

May 11, 2019 · I understand P ∧ Q, being that both must be equivalent, ie True & True, or False and False. I understand P --> Q implies that if P is True we know what Q is and if Q is true then the …

I have difficulties understanding why $ P \\implies Q$ is equivalent to P only if Q. I do understand that in the statement "P only if Q", it means if $ \\lnot Q \\implies \\lnot P$". Regarding this e...

Aug 7, 2021 · The p implies q statement is often described in various ways including: (1) if p then q (i.e. whenever p is true, q is true) (2) p only if q (i.e. whenever q is false, p is false) I see the truth t...

Aug 8, 2023 · I see the the truth table for $\text {if}\ P, \text {then}\ Q$. What does this mean when I see this in an example and what is the truth table for it? $$P ...

Jan 14, 2016 · A formal proof that this is a tautology would be written as proof : (p, p -> q) -> q proof (x, f) = f x and has the handy property of being automatically checkable on a PC by proof systems such …