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Which of the following is an example of a valid argument?Question 7Select one:A.If Kim plays, then Sandy won't play. If Sandy plays, then Kelly will be happy. So if Kim plays, Kelly won't be happy.B.Sandy won't play without Kim, and Kelly won't play without Sandy. Logically, the only thing to do is to have them all play.C.If Kim doesn't play, then Sandy won't play, either. If Sandy doesn't play, then Kelly won't play. So Kim won't play.D.If Kim doesn't play then Sandy will play instead. If Sandy plays, then Kelly will be happy. So if Kim doesn't play, Kelly will be happy.E.Kim and Sandy won't play, but Kelly will. If Kelly plays, we'll win. Too bad for Kim and Sandy.

Question

Which of the following is an example of a valid argument?Question 7Select one:A.If Kim plays, then Sandy won't play. If Sandy plays, then Kelly will be happy. So if Kim plays, Kelly won't be happy.B.Sandy won't play without Kim, and Kelly won't play without Sandy. Logically, the only thing to do is to have them all play.C.If Kim doesn't play, then Sandy won't play, either. If Sandy doesn't play, then Kelly won't play. So Kim won't play.D.If Kim doesn't play then Sandy will play instead. If Sandy plays, then Kelly will be happy. So if Kim doesn't play, Kelly will be happy.E.Kim and Sandy won't play, but Kelly will. If Kelly plays, we'll win. Too bad for Kim and Sandy.

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Solution

The valid argument in this case is D. "If Kim doesn't play then Sandy will play instead. If Sandy plays, then Kelly will be happy. So if Kim doesn't play, Kelly will be happy." This is a valid argument because the conclusion follows logically from the premises. If the premises are true (Kim doesn't play, leading to Sandy playing, and Sandy playing leads to Kelly being happy), then the conclusion must also be true (If Kim doesn't play, Kelly will be happy).

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