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I'm currently learning propositional logic and was wondering if I could rewrite the first statement as second (just less paranthesis)? Could it be interpreted as a totally different statement or it is fine as it is?

bsbb4
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Fl1pp
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    How are you planning to avoid $(A \land B \to C \land D)$ being read by some as possibly meaning $(A \land (B \to C) \land D)$? – Henry Sep 14 '19 at 18:12
  • You are right, thanks. I saw an example alike in the homework I have, hence the confusion. – Fl1pp Sep 14 '19 at 18:15
  • Follow up question, can't we use this order of precedence (¬, ∧, ∨, ⟹, ⟺) to avoid such a confusion? – Fl1pp Sep 14 '19 at 18:33
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    To expand on @Henry's comment, note that $(A\land B)\to(C\land D)$ is inequivalent to $A\land(B\to C)\land D$ because e.g. if $A,,B,,C,,D$ are all false then $(A\land B)\to(C\land D)$ is true but $A\land(B\to C)\land D$ is false. – J.G. Sep 14 '19 at 19:27

1 Answers1

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Consider when $A$ is false but $B$, $C$, and $D$ are true.

Shaun
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