I am struggling to understand truth sets and the symbols used.
In this context $P, Q, R$ are truth sets of $p,q,r$.
I am unsure of how to find the truth set of this expression $$ (p ∧ q) \to \neg r $$ And how to represent in a venn diagram
Would the diagram be something like this?
See Lipschutz, Schaum's Outline Of Discrete mathematics ( Index : " truth set").
The truth set of a proposition is the set of all cases in which this proposition is true.
Here, the " cases" are represented by lists ( ordered sets) of truth-values ( True/False): couples of truth-values if your formula has 2 atomic propositions, triples of truth-values if it has 3, etc.
So the truth set of a formula is a set of couples, or a set of triples, etc. ( depending on the number of atomic propositions involved in the formula).
To construct your Venn diagram, use as U ( universal set) the set of all possible couples, triples, etc.
Example ( with, by convention, P as first sentence and Q as second sentence)
The truth set of (P&Q) is { (T,T)} ( a set with only one element, for (P&Q) is true in only one case, namely the case in which P is true and Q is also true.
The truth set of (P v Q) is { (T,T), (T,F), (F,T)}
etc.
The formula (P&Q) => Q is valid ( is a tautology) since it's truth set is :
in other words, the formula is valid, since it's truth set is U, the universal set itself ( for a formula involving only 2 atomic sentences)!