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I'm trying to write a predicate logic for this statement but I'm not sure if I'm writing this correctly. Can anyone validate and let me know if this is correct and if not, help to come up with the correct syntax, please. Thanks in advance.

∀x (P(x) (A(x) ^ (H(x)) -----> Accumulation(bad cholesterol(x))

Lack of physical activity and high calorie diet can lead to accumulation of bad cholesterol.

Kifayat
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1 Answers1

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You have the right idea: First, translate the information into predicates. Let $A(x)$ be physical activity, $B(x)$ be high calories and $C(x)$ be accumulation of cholesterol. You want to say for every $x$ if $\neg A(x) \land B(x)$ are satisfied, $C(x)$ is as well. That is: $$ \forall x, [(\neg A(x) \land B(x)) \rightarrow C(x)] $$

We can interpret this as saying, "for every entity $x$, if $x$ lacks physical activity and has a high calorie diet, then $x$ will accumulate cholesterol."

Evan Rosica
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  • Thank you so much for your quick response. How would I translate this results? – Kifayat Nov 01 '18 at 18:05
  • translate to what? – Evan Rosica Nov 01 '18 at 18:05
  • Would this reads like this: For every entity x, if x lack physical activity and high calorie diet, then x can lead to accumulation of cholesterol. – Kifayat Nov 01 '18 at 18:07
  • I wouldn't say $x$ leads to accumulation, because then it sounds like $x$ is causing the accumulation. I'd say "For every entity $x$, if $x$ lacks physical activity and has a high calorie diet, then $x$ will accumulate cholesterol. – Evan Rosica Nov 01 '18 at 18:10
  • Awesome, thanks again! – Kifayat Nov 01 '18 at 18:12
  • @Evan, don't ask for an accept vote for your answer less than one-half hour of the question has been posted, and only 15 minutes after posting your answer. – amWhy Nov 01 '18 at 18:59