I am new in logic and I getting a little bit confused with maths. Can I do something like this following the Associative Law?
$$(p ∨ ¬r) ∨ (r ∨ ¬p) ≡ (p ∨ ¬p) ∨ (r ∨ ¬r)$$
Thank you in advance for your help
2026-03-26 09:36:52.1774517812
Proof for association law?
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Always go back to the (intuitive) intended meaning of the logical symbols. "$P \lor Q$" is true exactly when either "$P$" or "$Q$" is true (or both), which is also equivalent to that at least one of "$P$" or "$Q$" is true.
Now it is then clear that $( P \lor Q ) \lor R$ is going to be true exactly when at least one of $P,Q,R$ is true, and the order and arrangement do not matter.