Use your knowledge of the definitions of validity, soundness, strength, and cogency to determine which of the following statements are true. Check all that apply. A statement is either valid or invalid. If an inductive argument is weak, then the argument's premises cannot all be true. All valid deductive arguments are equally valid. If a deductive argument's premises are not all true, then you know that the argument must be unsound. If an inductive argument has true premises and a false conclusion, then the conclusion still could be strong, as long as the conclusion is unlikely to be false. An inductive argument cannot be both strong and uncogent. Some inductive arguments are stronger than others. A deductive argument cannot be both invalid and sound. In a cogent inductive argument, the conclusion is probably true. It is possible for an inductive argument to be both uncogent and strong. If the conclusion of a deductive argument is true, then you know that the argument is sound. Some inductive arguments are both strong and weak. If a deductive argument is unsound, then the argument's premises must all be false. In a valid deductive argument it is impossible for the premises to be true and the conclusion to be false simultaneously. A cogent argument that has a large degree of inductive strength could still have a conclusion that is actually false.

The true statements are:

1. A statement is either valid or invalid.

False

2. If an inductive argument is weak, then the argument's premises cannot all be true.

True

3. All valid deductive arguments are equally valid.

True

4. If a deductive argument's premises are not all true, then you know that the argument must be unsound.

True

5. If an inductive argument has true premises and a false conclusion, then the conclusion still could be strong, as long as the conclusion is unlikely to be false.

False

5. An inductive argument cannot be both strong and uncogent.

True

6. Some inductive arguments are stronger than others.

True

7. A deductive argument cannot be both invalid and sound.

True

8. In a cogent inductive argument, the conclusion is probably true.

False

9. It is possible for an inductive argument to be both uncogent and strong.

False

10. If the conclusion of a deductive argument is true, then you know that the argument is sound.

True

11. Some inductive arguments are both strong and weak.

False

12. If a deductive argument is unsound, then the argument's premises must all be false.

True.

13. In a valid deductive argument it is impossible for the premises to be true and the conclusion to be false simultaneously.

True

14. A cogent argument that has a large degree of inductive strength could still have a conclusion that is actually false.

True

Explanation:

A statement is either true or untrue.  A statement cannot be valid or invalid.  Validity, soundness, strength, and cogency apply to arguments and not to statements.  When one makes a valid argument, it is impossible for the premises to be true and the conclusion false.

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