Is the following argument valid? If so, construct a formal proof (direct or indirect). If not,...

Is the following argument valid? If so, construct a formal proof (direct or indirect). If not, explain why not.

If Alex gets a new job, then he will buy a guitar.

If Alex wins the lottery, then he will buy a guitar.

If Alex goes to Costa Rica, then either Alex got a new job or Alex won the lottery.

Alex goes to Costa Rica.

Therefore, Alex bought a guitar.

Solutions

Expert Solution

The given argument is correct.

Argument is that,

Alex goes to Costa Rica. Therefore, Alex bought a guitar.

Proof: Given that Alex goes to Costa Rica.

We know that if Alex goes to Costa Rica, then either Alex got a new job or Alex won the lottery.

Then we know that in either case, that is either he gets a new job or he wins a lottery then he will buy a guitar. Therefore we can conclude that if Alex goes to Costa Rica then he will surely bye a guitar.

Therefore the given argument is valid.

orchestra answered 1 year ago

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