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7. Arik promised to help out if we needed him. So he didn't help out.

Missing premise: But we didn't need him

Conclusion: We didn't need him.

Conclusion: Arik broke his promise.

Invalid.

8. Yalli refused to buy the car if he couldn't drive it first. So he didn't buy it.

Missing premise: Yalli couldn't drive the car first.

Missing premise: Yalli couldn't buy the car.

Conclusion: Yalli refused to buy the car.

Invalid.

9. If Georgia really loved him, she wouldn't have left. So I guess she didn't really love him.

Missing premise: Georgia didn't love him.

Missing premise: Georgia left.

Missing premise: Georgia didn't leave.

Invalid.

10. If Kazuo had gotten a few breaks, he could have been a star. But he didn't get any breaks at all.

Missing premise: He'll never be a star.

Conclusion: He couldn't get that reservation.

Conclusion: So he couldn't have been a star.

Invalid.

7. Arik promised to help out if we needed him. So he didn't help out.

You answered:

Invalid.

Correct!

This is yet another variation of the invalid form seen in questions 5 and 6 above.

The first premise, again, is the conditional "If we needed him (p), Arik promised to help out (q)." The two possible valid conclusions for that conditional are:

modus ponens: needed (p), therefore helped (q)
and
modus tollens: didn't help (not q), therefore wasn't needed (not p).
But the conclusion given, "didn't help (not q)," is neither of these, and so whatever missing premise is supplied, the argument must be invalid.

8. Yalli refused to buy the car if he couldn't drive it first. So he didn't buy it.

You answered:

Missing premise: Yalli couldn't drive the car first.

Correct!

The first premise, re-ordered, is the conditional, "If he couldn't drive it first (p), Yalli refused to buy the car (q)." And the stated conclusion is, "So he didn't buy it" [that is, "refused to buy it" (q)].

In this case, the valid paradigm is:

If p (not drive), then q (not buy).
P (not drive).
Therefore, q (not buy)
Notice two things about the negatives in this argument: First, that negatives in the conditional premise must be incorporated into the antecedent or the consequent. Here, for example, "not drive" is "p" and not "not p." And second, that some negatives can be expressed without the use of "no" or "not." Here, "refused to buy" is the equivalent of "did not buy."

9. If Georgia really loved him, she wouldn't have left. So I guess she didn't really love him.

You answered:

Missing premise: Georgia left.

Correct!

The first premise, re-ordered, is the conditional, "If he couldn't drive it first (p), Yalli refused to buy the car (q)." And the stated conclusion is, "So he didn't buy it" [that is, "refused to buy it" (q)].

In this case, the valid paradigm is:

If p (not drive), then q (not buy).
P (not drive).
Therefore, q (not buy)
Notice two things about the negatives in this argument: First, that negatives in the conditional premise must be incorporated into the antecedent or the consequent. Here, for example, "not drive" is "p" and not "not p." And second, that some negatives can be expressed without the use of "no" or "not." Here, "refused to buy" is the equivalent of "did not buy."

10. If Kazuo had gotten a few breaks, he could have been a star. But he didn't get any breaks at all.

You answered:

Invalid.

Correct!

Another invalid argument. The first premise is the conditional, "If Kazuo had gotten a few breaks (p), then he could have been a star (q)." But the second premise negates the antecedent, "But he didn't get any breaks at all (not p)." The only choices for a valid second premise are p ("got breaks"), and not q ("not a star").

7. Arik promised to help out if we needed him. So he didn't help out.

You answered:

Missing premise: But we didn't need him.

This is yet another variation of the invalid form seen in questions 5 and 6 above.

The first premise, again, is the conditional "If we needed him (p), Arik promised to help out (q)." The two possible valid conclusions for that conditional are:

modus ponens: needed (p), therefore helped (q)
and
modus tollens: didn't help (not q), therefore wasn't needed (not p).
But the conclusion given, "didn't help (not q)," is neither of these, and so whatever missing premise is supplied, the argument must be invalid.

7. Arik promised to help out if we needed him. So he didn't help out.

You answered:

Conclusion: We didn't need him.

This is yet another variation of the invalid form seen in questions 5 and 6 above.

The first premise, again, is the conditional "If we needed him (p), Arik promised to help out (q)." The two possible valid conclusions for that conditional are:

modus ponens: needed (p), therefore helped (q)
and
modus tollens: didn't help (not q), therefore wasn't needed (not p).
But the conclusion given, "didn't help (not q)," is neither of these, and so whatever missing premise is supplied, the argument must be invalid.

7. Arik promised to help out if we needed him. So he didn't help out.

You answered:

Conclusion: Arik broke his promise.

This is yet another variation of the invalid form seen in questions 5 and 6 above.

The first premise, again, is the conditional "If we needed him (p), Arik promised to help out (q)." The two possible valid conclusions for that conditional are:

modus ponens: needed (p), therefore helped (q)
and
modus tollens: didn't help (not q), therefore wasn't needed (not p).
But the conclusion given, "didn't help (not q)," is neither of these, and so whatever missing premise is supplied, the argument must be invalid.

8. Yalli refused to buy the car if he couldn't drive it first. So he didn't buy it.

You answered:

Missing premise: Yalli couldn't buy the car.

You can make this a valid argument by supplying the correct missing premise." But the negatives here may have confused you.

The first premise, re-ordered, is the conditional, "If he couldn't drive it first (p), Yalli refused to buy the car (q)." And the stated conclusion is, "So he didn't buy it" [that is, "refused to buy it" (q)].

In this case, the valid paradigm is:

If p (not drive), then q (not buy).
P (not drive).
Therefore, q (not buy)
Notice two things about the negatives in this argument: First, that negatives in the conditional premise must be incorporated into the antecedent or the consequent. Here, for example, "not drive" is "p" and not "not p." And second, that some negatives can be expressed without the use of "no" or "not." Here, "refused to buy" is the equivalent of "did not buy."

8. Yalli refused to buy the car if he couldn't drive it first. So he didn't buy it.

You answered:

Conclusion: Yalli refused to buy the car.

You can make this a valid argument by supplying the correct missing premise." But the negatives here may have confused you.

The first premise, re-ordered, is the conditional, "If he couldn't drive it first (p), Yalli refused to buy the car (q)." And the stated conclusion is, "So he didn't buy it" [that is, "refused to buy it" (q)].

In this case, the valid paradigm is:

If p (not drive), then q (not buy).
P (not drive).
Therefore, q (not buy)
Notice two things about the negatives in this argument: First, that negatives in the conditional premise must be incorporated into the antecedent or the consequent. Here, for example, "not drive" is "p" and not "not p." And second, that some negatives can be expressed without the use of "no" or "not." Here, "refused to buy" is the equivalent of "did not buy."

8. Yalli refused to buy the car if he couldn't drive it first. So he didn't buy it.

You answered:

Invalid.

You can make this a valid argument by supplying the correct missing premise." But the negatives here may have confused you.

The first premise, re-ordered, is the conditional, "If he couldn't drive it first (p), Yalli refused to buy the car (q)." And the stated conclusion is, "So he didn't buy it" [that is, "refused to buy it" (q)].

In this case, the valid paradigm is:

If p (not drive), then q (not buy).
P (not drive).
Therefore, q (not buy)
Notice two things about the negatives in this argument: First, that negatives in the conditional premise must be incorporated into the antecedent or the consequent. Here, for example, "not drive" is "p" and not "not p." And second, that some negatives can be expressed without the use of "no" or "not." Here, "refused to buy" is the equivalent of "did not buy."

9. If Georgia really loved him, she wouldn't have left. So I guess she didn't really love him.

You answered:

Missing premise: Georgia didn't love him.

You can make this a valid argument by supplying the missing premise. The first premise is the conditional, "If Georgia really loved him (p), then she would not have left (q)." And the stated conclusion is, "So I guess she didn't really love him (not p)." In order to conclude "not p" validly, the second premise must be "not q" (modus tollens). So the paradigm would be:

If p (loved him), then q (not leave).
Not Q (left).
Therefore, not p (did not love him).
Notice here that a positive ("left") becomes not q, and is used to negate a consequent that contains a negative ("not leave").

9. If Georgia really loved him, she wouldn't have left. So I guess she didn't really love him.

You answered:

Missing premise: Georgia didn't leave.

You can make this a valid argument by supplying the missing premise. The first premise is the conditional, "If Georgia really loved him (p), then she would not have left (q)." And the stated conclusion is, "So I guess she didn't really love him (not p)." In order to conclude "not p" validly, the second premise must be "not q" (modus tollens). So the paradigm would be:

If p (loved him), then q (not leave).
Not Q (left).
Therefore, not p (did not love him).
Notice here that a positive ("left") becomes not q, and is used to negate a consequent that contains a negative ("not leave").

9. If Georgia really loved him, she wouldn't have left. So I guess she didn't really love him.

You answered:

Invalid.

You can make this a valid argument by supplying the missing premise. The first premise is the conditional, "If Georgia really loved him (p), then she would not have left (q)." And the stated conclusion is, "So I guess she didn't really love him (not p)." In order to conclude "not p" validly, the second premise must be "not q" (modus tollens). So the paradigm would be:

If p (loved him), then q (not leave).
Not Q (left).
Therefore, not p (did not love him).
Notice here that a positive ("left") becomes not q, and is used to negate a consequent that contains a negative ("not leave").

10. If Kazuo had gotten a few breaks, he could have been a star. But he didn't get any breaks at all.

You answered:

Missing premise: He'll never be a star.

Another invalid argument. The first premise is the conditional, "If Kazuo had gotten a few breaks (p), then he could have been a star (q)." But the second premise negates the antecedent, "But he didn't get any breaks at all (not p)." The only choices for a valid second premise are p ("got breaks"), and not q ("not a star").

10. If Kazuo had gotten a few breaks, he could have been a star. But he didn't get any breaks at all.

You answered:

Conclusion: He couldn't get that reservation.

Another invalid argument. The first premise is the conditional, "If Kazuo had gotten a few breaks (p), then he could have been a star (q)." But the second premise negates the antecedent, "But he didn't get any breaks at all (not p)." The only choices for a valid second premise are p ("got breaks"), and not q ("not a star").

10. If Kazuo had gotten a few breaks, he could have been a star. But he didn't get any breaks at all.

You answered:

Conclusion: So he couldn't have been a star.

Another invalid argument. The first premise is the conditional, "If Kazuo had gotten a few breaks (p), then he could have been a star (q)." But the second premise negates the antecedent, "But he didn't get any breaks at all (not p)." The only choices for a valid second premise are p ("got breaks"), and not q ("not a star").

Congratulations! You have finished the exercises for the "Conditional Arguments" section.

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