I’m currently in intro to logic and we have been given questions where I don’t understand the vocabulary or process to getting the right answer. The questions come from the Forallx intro to logic online textbook and need to be solved using natural deduction rules in TFL form.
1. Show that the sentence ¬(X ∨ (Y ∨Z)) ∨ (X ∨ (Y ∨Z)) is not contingent
2. Show that A→(A→B) is not a theorem.
The problem with 1 and 2 are that I only know how to show when a sentence is contingent or a theorem, not when its not.
3. Show that ¬¬(C ↔ ¬C)
((G ∨C) ∨G)
∴ ((G → C) ∧G)
When I get to my second sub proof I run into the problem of being unable to Isolate C
4. Show that the sentences
¬(W → W)
(W ↔ W) ∧W
E ∨ (W → ¬(E ∧ W ))
are jointly inconsistent.
Here I don’t know what jointly means or how to represent it,
Any help would be appreciated!