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If the horse is fresh, then the knight will win. $H -> K$ A fresh horse is a necessary condition for the knight to win. $K -> H$

I think the first sentence should have same notation. I don't understand why are different.

Wolgwang
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Mike90s
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1 Answers1

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$p \implies q$ is not the same as $q \implies p$. $q \implies p$ is the converse of $p\implies q$. In other words they are not logically equivalent. Make a truth table and you’ll see why.

  • I understand the logical notation but the English from this sentence If the horse is fresh, then the knight will win. I understand that in order for the knight to win need the condition the horse to be fresh true.so I still don't understand first sentence is K−> H – Mike90s Nov 14 '20 at 08:28
  • I think that should be OK. There is a list of “if then” English equivalencies. Another way to look at this is to look at the truth table. $K \implies H$, $H$ has to be true for $K$ to be true (by a true table). That’s why $H$ is a necessary condition for $K$ (for this statement to be true). Is that clear, or no? –  Nov 14 '20 at 08:36
  • yes I understand but in this case "If the horse is fresh, then the knight will win. H−>K" mean that the horse to be fresh depends on the knight win. I think should be K -> H . Knight win depends if the horse is fresh (If the horse is fresh). – Mike90s Nov 14 '20 at 10:09