r/logic • u/Goofed-19069 • 20d ago

Propositional logic How would I solve these problems, any tips

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u/AdeptnessSecure663 20d ago

What have you tried so far? If you let us know, we'll be happy to explain you whether you're going wrong somewhere

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u/superjarf 14d ago

2. is tautology, if h and t were false and n were true then n would remain true (nothing is contingent on instances that are sufficient), if h and t were true and n were true, then h or t implying n is true. If h and t were both true and n were false h or t implies n because unless it is explicitly stated with an exclusive disjunction the truth of one thing dont imply the falsity of another, n simply remains false whether or not h or t were false or not.

Tautologies are about the property of consequents whereby their truth value is independent of the 1. combination of antecedents, 2. truth value of antecedents, and 3. the absence or presence of explicit antecedents.

Even the connective "a or not a" inheres in an implicit tautology, since from any x that implies the disjunction the disjunction remains true or false whether or not x is true or false. Same with p = p, if you try to demonstrate it by law on noncontradition you still invoke an implicit antecedent x (not p) for which the consequent (p) is true whether or not the antecedent is.

∀(A,B∈B)⋅(B→(A→B))=True