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This expression:

$1 \lor (0 \land 1 \land 1 \land 1 \land 1 \lor 0)$

Regardless of how order of operations inside the parentheses are taken, which are ambiguous, the fact that it is and Or operation with a 1 on the outside will always evaluate to true?

By the way, 1 represents true in this case, and 0 represents false.

op_finales
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  • $\land$ works like multiplication while $\lor$ works like addition. Then, $\land$ has to be performed before $\lor$. – the_candyman Mar 18 '16 at 18:11
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    If we’re being fussy, it is simply meaningless unless some convention has been established that allows the parenthesized expression to be evaluated. However, it’s perfectly true that once it has been given meaning by some such convention, it will always evaluate to $1$. – Brian M. Scott Mar 18 '16 at 18:11
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    @the_candyman: There is no such convention. – Brian M. Scott Mar 18 '16 at 18:12
  • @BrianM.Scott I'm aware that there are no convention. But if not specified, the common sense suggest that $\land$ must be performed before $\lor$. Just MHO. – the_candyman Mar 18 '16 at 18:13
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    @the_candyman But those are evaluated inside parentheses, so regardless of the outcome inside, it should evaluate to true because $1 \lor 0$ is 1 and $1 \lor 1$ is 1. – op_finales Mar 18 '16 at 18:13
  • @BrianM.Scott the result is obviously $1$, but I just remarked my opinion on the order of operations. Otherwise, I would have posted an answer with the solution. – the_candyman Mar 18 '16 at 18:15
  • @the_candyman: Alternatively, common sense may suggest that the expression be evaluated from left to right, since $\land$ and $\lor$ are dual operations and hence not really analogous to multiplication and addition, respectively. And no, the expression is technically undefined unless a rule for evaluating the parenthetical expression has previously been given. – Brian M. Scott Mar 18 '16 at 18:15
  • @the_candyman: $x \lor 0 = x$ like $x + 0 = x$. $x \land 0 = 0$ like $x \times 0 = 0$. $x \land 1 = x$ like $x \times 1 = x$. – the_candyman Mar 18 '16 at 18:16

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