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The question is:

If Bob is happy, then all his friends are happy

My attempt looks like:

$happy(bob) \Rightarrow (\forall x(friend(x, bob) \wedge happy(x)))$

The answer is

$happy(bob) \Rightarrow (\forall x(friend(x, bob) \color{red}{\Rightarrow} happy(x)))$

So is my answer acceptable too? If not why?

1 Answers 1

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Your answer translates into pseudo-logic as

If Bob is happy, then { for all $x$: $x$ is friends with Bob and $x$ is happy }

whereas what you want is

If Bob is happy, then { for all $x$: if $x$ is Bob's friend then $x$ is happy }

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    No - your answer says that *everyone* is friends with Bob. You need to say that people are happy *if* they are friends with Bob (which is why you need the implication). If someone is not friends with Bob, then we don't know if they're happy or unhappy.2012-09-28