Precedence and Implication (Propositional Logic) | Checking answer

[tired pivot]

So, they ask us to simplify boolean expressions.
On this one question, I simply the boolean question and I get to the "correct answer"... but I'm pretty sure I can continue simplifying.

I want to confirm I didn't do anything wrong so I've provided two images, the first one is the exact answer that was provided (notice the extra bracket at the end, I think my lecturer was drunk when writing the solution) and the other with my workings out (after reaching the "correct answer". I also state the law (I think) I used.

Can someone please just go through and confirm, say "yep that makes, the correct answer wasn't fully simplified, yours is" or "no, you can't simply further because of x".

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[tired pivot]

Nevermind, I managed to check my answer using truth tables (and Wolfgram Alpha)

p | q | r | (p ∧ q) ∨ r implies q ∨ (¬p ∧ r)
T | T | T | T
T | T | F | T
T | F | T | F
T | F | F | T
F | T | T | T
F | T | F | T
F | F | T | T
F | F | F | T

p | q | r | q ∨ ¬r ∨ ¬p
T | T | T | T
T | T | F | T
T | F | T | F
T | F | F | T
F | T | T | T
F | T | F | T
F | F | T | T
F | F | F | T

Happy days, seems like my lecturer was drunk and also it seems I do understand propositional logical laws. 👍

+close