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Exercises on Conditionals

Instructions: For each of the following, determine whether the argument can be valid. If so, supply the conclusion or missing premise that would make it a valid argument. If not, choose "invalid" for your answer.

1. If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

Conclusion: You should be able to complete these exercises.

Conclusion: You should not be able to complete these exercises.

Conclusion: You haven't really read the introduction.

Invalid.

2. If Sunetra read the introduction, she should be able to do these exercises. So she should be able to do these exercises.

Missing premise: She did not read the introduction.

Missing premise: She read the introduction.

Conclusion: She read the introduction.

Invalid.

3. If my dog could talk, she would have interesting things to say. But she can't talk.

Missing premise: She has nothing interesting to say.

Conclusion: She has interesting things to say.

Conclusion: She has nothing interesting to say.

Invalid.

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

Choose "Advanced Conditionals" to deal with more complex conditionals, "Syllogisms" to deal with another form of deduction, or "Main Menu" to go on with a different section.

Main Menu --Advanced Conditionals--Unqualified Syllogisms

1. If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

You answered:

Conclusion: You should be able to complete these exercises.

Correct!

The first premise is the conditional:

If you have read the introduction (p), then you should be able to complete these exercises (q).
And the second premise is given as:
And you have read the introduction.

So the paradigm is:

  • If p (read intro), then q (complete exercises).
  • P (read intro).
  • Therefore, q (complete exercises).

Notice here that a conjunction ("and" or "but") can often serve to introduce a premise, by indicating that the claim following is on the same logical level as the conditional premise which preceded it.

2. If Sunetra read the introduction, she should be able to do these exercises. So she should be able to do these exercises.

You answered:

Missing premise: She read the introduction.

Correct!

The first premise is the conditional:
If Sunetra read the introduction (p), then she should be able to do these exercises (q).
And the second claim is indentified as the conclusion by the indicator, "so":
So she should be able to do these exercises (q).

So the paradigm is:

If p (read intro), then q (do exercises).
P (read intro). [unstated premise]
Therefore, q (do exercises).

3. If my dog could talk, she would have interesting things to say. But she can't talk.

You answered:

Invalid.

Correct!

This argument is in an invalid form, no matter what that dog says, because the second premise negates the antecedent.

You can make a valid argument here by adding the unstated premise, "She read the introduction."

The first premise is the conditional, "If my dog could talk (p), then she would have interesting things to say (q)." The two possibilities for a valid second premise are affirming the antecedent (p), "My dog can talk," or negating the consequent (q), "She won't have interesting things to say." But the claim given, "She can't talk" fits neither of the valid possibilities, so the argument must be invalid.

1. If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

You answered:

Conclusion: You should not be able to complete these exercises.

The first premise is the conditional:

If you have read the introduction (p), then you should be able to complete these exercises (q).
And the second premise is given as:
And you have read the introduction.

So the paradigm is:

  • If p (read intro), then q (complete exercises).
  • P (read intro).
  • Therefore, q (complete exercises).

Notice here that a conjunction ("and" or "but") can often serve to introduce a premise, by indicating that the claim following is on the same logical level as the conditional premise which preceded it.

1. If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

You answered:

Conclusion: You haven't really read the introduction.

The first premise is the conditional:

If you have read the introduction (p), then you should be able to complete these exercises (q).
And the second premise is given as:
And you have read the introduction.

So the paradigm is:

  • If p (read intro), then q (complete exercises).
  • P (read intro).
  • Therefore, q (complete exercises).

Notice here that a conjunction ("and" or "but") can often serve to introduce a premise, by indicating that the claim following is on the same logical level as the conditional premise which preceded it.

1. If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

You answered:

Invalid.

The first premise is the conditional:

If you have read the introduction (p), then you should be able to complete these exercises (q).
And the second premise is given as:
And you have read the introduction.

So the paradigm is:

  • If p (read intro), then q (complete exercises).
  • P (read intro).
  • Therefore, q (complete exercises).

Notice here that a conjunction ("and" or "but") can often serve to introduce a premise, by indicating that the claim following is on the same logical level as the conditional premise which preceded it.

2. If Sunetra read the introduction, she should be able to do these exercises. So she should be able to do these exercises.

You answered:

Missing premise: She did not read the introduction.

The first premise is the conditional:

If Sunetra read the introduction (p), then she should be able to do these exercises (q).
And the second claim is indentified as the conclusion by the indicator, "so":
So she should be able to do these exercises (q).

So the paradigm is:

If p (read intro), then q (do exercises).
P (read intro). [unstated premise]
Therefore, q (do exercises).

2. If Sunetra read the introduction, she should be able to do these exercises. So she should be able to do these exercises.

You answered:

Conclusion: She read the introduction.

The first premise is the conditional:

If Sunetra read the introduction (p), then she should be able to do these exercises (q).
And the second claim is indentified as the conclusion by the indicator, "so":
So she should be able to do these exercises (q).

So the paradigm is:

If p (read intro), then q (do exercises).
P (read intro). [unstated premise]
Therefore, q (do exercises).

2. If Sunetra read the introduction, she should be able to do these exercises. So she should be able to do these exercises.

You answered:

Invalid.

The first premise is the conditional:

If Sunetra read the introduction (p), then she should be able to do these exercises (q).
And the second claim is indentified as the conclusion by the indicator, "so":
So she should be able to do these exercises (q).

So the paradigm is:

If p (read intro), then q (do exercises).
P (read intro). [unstated premise]
Therefore, q (do exercises).

3. If my dog could talk, she would have interesting things to say. But she can't talk.

You answered:

Missing premise: She has nothing interesting to say.

This argument is in an invalid form, no matter what that dog says, because the second premise negates the antecedent.

You can make a valid argument here by adding the unstated premise, "She read the introduction."

The first premise is the conditional, "If my dog could talk (p), then she would have interesting things to say (q)." The two possibilities for a valid second premise are affirming the antecedent (p), "My dog can talk," or negating the consequent (q), "She won't have interesting things to say." But the claim given, "She can't talk" fits neither of the valid possibilities, so the argument must be invalid.

3. If my dog could talk, she would have interesting things to say. But she can't talk.

You answered:

Conclusion: She has interesting things to say.

This argument is in an invalid form, no matter what that dog says, because the second premise negates the antecedent.

You can make a valid argument here by adding the unstated premise, "She read the introduction."

The first premise is the conditional, "If my dog could talk (p), then she would have interesting things to say (q)." The two possibilities for a valid second premise are affirming the antecedent (p), "My dog can talk," or negating the consequent (q), "She won't have interesting things to say." But the claim given, "She can't talk" fits neither of the valid possibilities, so the argument must be invalid.

3. If my dog could talk, she would have interesting things to say. But she can't talk.

You answered:

Conclusion: She has nothing interesting to say.

This argument is in an invalid form, no matter what that dog says, because the second premise negates the antecedent.

You can make a valid argument here by adding the unstated premise, "She read the introduction."

The first premise is the conditional, "If my dog could talk (p), then she would have interesting things to say (q)." The two possibilities for a valid second premise are affirming the antecedent (p), "My dog can talk," or negating the consequent (q), "She won't have interesting things to say." But the claim given, "She can't talk" fits neither of the valid possibilities, so the argument must be invalid.