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Question: Which one of the first-order predicate calculus statements given below correctly expresses the statement “Tigers and lions attack if they are hungry or threatened”?

Answer: $∀x[($tiger$(x) ∨$ lion$(x))→$ (hungry$(x) ∨$ threatened$(x))→$ attacks$(x)]$

Please explain to me why "tigers and lions" converts to "tiger$(x) ∨$ lion$(x)$" instead of "tiger$(x) ∧$ lion$(x)$".

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ryang
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Feb 14 '22 at 09:07
  • Actually two statements are made. One about tigers ($\forall x\in T p(x)$) and one about lions ($\forall x\in L p(x)$). Expressing both in one statement we get $\forall x\in T\cup L p(x)$. – drhab Feb 14 '22 at 09:18
  • Because no animal is both a tiger and a lion. – Mauro ALLEGRANZA Feb 14 '22 at 09:50

1 Answers1

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“Tigers and lions attack if they are hungry or threatened”

Since all four given options offer the predicate "attacks" instead of "attack", the above statement is not meant to be read literally as referring to a combined attack. The intended meaning must be “every tiger attacks if it is hungry or threatened, and every lion attacks if it is hungry or threatened”.

This is equivalent to “every tiger or lion attacks if it is hungry or threatened”, in other words, “every tiger or lion, if it is hungry or threatened, attacks”.

This translates as $∀x[($tiger$(x) ∨$ lion$(x))→ \bigg(($hungry$(x) ∨$ threatened$(x))→$ attacks$(x)\bigg)].$ Since the conditional symbol is right-associative, we can drop that pair of big parentheses:

A. $∀x[($tiger$(x) ∨$ lion$(x))→$ (hungry$(x) ∨$ threatened$(x))→$ attacks$(x)]$

P.S. This correct answer is not equivalent to $∀x[\bigg(($tiger$(x) ∨$ lion$(x))→ ($hungry$(x) ∨$ threatened$(x))\bigg)→$ attacks$(x)].$

P.P.S. Regarding the conversion of the above boldfaced words: if $C$ is the set of tigers and lions, then each element of $C$ must be either a tiger or a lion.

ryang
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