Let {A1, A2, A3, ... } be an infinite set of formulas in propositional logic. Assume that(adsbygoogle = window.adsbygoogle || []).push({});

for every valuation v there is some n (depending on v) such that v(An) = 1. Show

then that there is some fixed m with A1 [tex]\vee[/tex] A2 [tex]\vee[/tex] ... [tex]\vee[/tex] Am a tautology.

This is equivalent to showing that v(Ai) = 1 for at least one 1[tex]\leq[/tex]i[tex]\leq[/tex]m. But I'm not sure where to proceed from here.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Infinite set, disjunction, and tautology

**Physics Forums | Science Articles, Homework Help, Discussion**