Propositional Logic, Resolution - derived tautology from 2 clauses of cardinality 3... I have 2 clauses of cardinality 3 $$(a \lor b \lor c)\land(a \lor \lnot b \lor\lnot c)$$ or, in set notation $$\\{a, b, c\\}, \\{a, \lnot b, \lnot c\\}$$ I applied _resolution_ **incorrectly** and got clause $$\\{a\\}$$ Now, someone told me that if we apply _resolution_ on these 2 clauses we get a _tautology_ , but I don't understand why/how. Can someone please explain? Thank you.

You only resolve on one literal. This was your mistake: you resolved on _both_ $b$ and $c$, but you can only resolve on one of them.

Now, if you resolve on $b$, the result is $\\{a,c,\
eg c\\}$, which is indeed a tautology, since whether $c$ is true or false, this clause will always be satisfied: it is a tautologous clause.

Likewise, if you resolve on $c$, the result is $\\{a , b , \
eg b\\}$, which is a tautologous clause as well.