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4. Peter was supposed to be here on Friday, if he could get a reservation on the morning flight. And he never arrived.

Missing premise: He couldn't get that reservation.

Conclusion: He couldn't get that reservation.

Conclusion: He wasn't supposed to be here on Friday.

Invalid.

5. There would be peace on earth today, if people would just try to communicate with each other. But they don't.

Missing premise: There's no peace on earth.

Conclusion: There's no peace on earth.

Conclusion: People should try to communicate with each other.

Invalid.

6. If Sophia had any ambition, she would have stayed in school. So she dropped out.

Missing premise: She had no ambition.

Missing premise: She had some ambition, but not enough.

Conclusion: She had no ambition.

Invalid.

4. Peter was supposed to be here on Friday, if he could get a reservation on the morning flight. And he never arrived.

You answered:

Conclusion: He couldn't get that reservation.

Correct!

Remember that the antecedent follows the conditional "if." The first premise, re-ordered, is the conditional, "If he could get a reservation on the morning flight (p), then Peter was supposed to be here on Friday (q)." And the second claim is, "And he never arrived (not q)." So the paradigm is:

If p (reservation), then q (arrive).
Not q (not arrive).
Therefore, not p (no reservation).

5. There would be peace on earth today, if people would just try to communicate with each other. But they don't.

You answered:

Invalid.

Correct!

This is another example of negating the antecedent, which is invalid. The first premise, re-ordered, is the conditional, "If people would just try to communicate with each other (p), then there would be peace on earth today (q)." And the second claim is, "But they don't [try to communicate] (not p)."

Sometimes, we mistakenly understand a conditional to be bi-directional. In this case, for example, we might misunderstand the first premise to mean "if communication, then peace," and "if peace, then communication." But it is dangerous to jump to such a conclusion, unless there is specific wording to support such a reading. Here there is none, and the argument is invalid, regardless of its conclusion.

6. If Sophia had any ambition, she would have stayed in school. So she dropped out.

You answered:

Invalid.

Correct!

The first premise, as always, is the conditional: "If Sophia had any ambition (p), then she would have stayed in school (q)." The two possible valid arguments for that conditional are:
modus tollens: didn't stay (not q), therefore no ambition (not p)
and
modus ponens: ambition (p), therefore stayed (q).
Neither of these valid arguments end in the conclusion given, "So she dropped out," and therefore that must be an invalid conclusion.

4. Peter was supposed to be here on Friday, if he could get a reservation on the morning flight. And he never arrived.

You answered:

Missing premise: He couldn't get that reservation.

Remember that the antecedent follows the conditional "if." In this case, a valid conclusion can be drawn. The first premise, re-ordered, is the conditional "If he could get a reservation on the morning flight (p), then Peter was supposed to be here on Friday (q)." And the second claim is: "And he never arrived (not q)." So the paradigm is:

If p (reservation), then q (arrive).
Not q (not arrive).
Therefore, not p (no reservation).

4. Peter was supposed to be here on Friday, if he could get a reservation on the morning flight. And he never arrived.

You answered:

Conclusion: He wasn't supposed to be here on Friday.

Remember that the antecedent follows the conditional "if." The first premise, re-ordered, is the conditional "If he could get a reservation on the morning flight (p), then Peter was supposed to be here on Friday (q)." And the second claim is: "And he never arrived (not q)." So the paradigm is:

If p (reservation), then q (arrive).
Not q (not arrive).
Therefore, not p (no reservation).

4. Peter was supposed to be here on Friday, if he could get a reservation on the morning flight. And he never arrived.

You answered:

Invalid.

Remember that the antecedent follows the conditional "if." In this case, a valid conclusion can be drawn.

The first premise, re-ordered, is the conditional "If he could get a reservation on the morning flight (p), then Peter was supposed to be here on Friday (q)." And the second claim is: "And he never arrived (not q)." So the paradigm is:

If p (reservation), then q (arrive).
Not q (not arrive).
Therefore, not p (no reservation).

5. There would be peace on earth today, if people would just try to communicate with each other. But they don't.

You answered:

Missing premise: There's no peace on earth.

This is another example of negating the antecedent, which is invalid. The first premise, re-ordered, is the conditional, "If people would just try to communicate with each other (p), then there would be peace on earth today (q)." And the second claim is, "But they don't [try to communicate] (not p)."

Sometimes, we mistakenly understand a conditional to be bi-directional. In this case, for example, we might misunderstand the first premise to mean "if communication, then peace," and "if peace, then communication." But it is dangerous to jump to such a conclusion, unless there is specific wording to support such a reading. Here there is none, and the argument is invalid, regardless of its conclusion.

5. There would be peace on earth today, if people would just try to communicate with each other. But they don't.

You answered:

Conclusion: There's no peace on earth.

This is another example of negating the antecedent, which is invalid. The first premise, re-ordered, is the conditional, "If people would just try to communicate with each other (p), then there would be peace on earth today (q)." And the second claim is, "But they don't [try to communicate] (not p)."

Sometimes, we mistakenly understand a conditional to be bi-directional. In this case, for example, we might misunderstand the first premise to mean "if communication, then peace," and "if peace, then communication." But it is dangerous to jump to such a conclusion, unless there is specific wording to support such a reading. Here there is none, and the argument is invalid, regardless of its conclusion.

5. There would be peace on earth today, if people would just try to communicate with each other. But they don't.

You answered:

Conclusion: People should try to communicate with each other.

This is another example of negating the antecedent, which is invalid. The first premise, re-ordered, is the conditional, "If people would just try to communicate with each other (p), then there would be peace on earth today (q)." And the second claim is, "But they don't [try to communicate] (not p)."

Sometimes, we mistakenly understand a conditional to be bi-directional. In this case, for example, we might misunderstand the first premise to mean "if communication, then peace," and "if peace, then communication." But it is dangerous to jump to such a conclusion, unless there is specific wording to support such a reading. Here there is none, and the argument is invalid, regardless of its conclusion.

6. If Sophia had any ambition, she would have stayed in school. So she dropped out.

You answered:

Missing premise: She had no ambition.

The first premise, as always, is the conditional: "If Sophia had any ambition (p), then she would have stayed in school (q)." The two possible valid arguments for that conditional are:

modus tollens: didn't stay (not q), therefore no ambition (not p)
and
modus ponens: ambition (p), therefore stayed (q).
So your answer, "no ambition," makes an invalid argument.

6. If Sophia had any ambition, she would have stayed in school. So she dropped out.

You answered:

Missing premise: She had some ambition, but not enough.

The first premise, as always, is the conditional: "If Sophia had any ambition (p), then she would have stayed in school (q)." The two possible valid arguments for that conditional are:

modus tollens: didn't stay (not q), therefore no ambition (not p)
and
modus ponens: ambition (p), therefore stayed (q).
"Some ambition" would be logically equivalent to "ambition," and then your answer would be correct; but "some ambition, but not enough" would be equivalent to "no ambition," and would not create a valid argument.

6. If Sophia had any ambition, she would have stayed in school. So she dropped out.

You answered:

Conclusion: She had no ambition.

The first premise, as always, is the conditional: "If Sophia had any ambition (p), then she would have stayed in school (q)." The two possible valid arguments for that conditional are:

modus tollens: didn't stay (not q), therefore no ambition (not p)
and
modus ponens: ambition (p), therefore stayed (q).
You chose the conclusion, "She had no ambition," but the question already included a conclusion, "So she dropped out." Remember to use premise and conclusion indicators, like "so," to help identify the parts of an argument.