Choose the best answer.

"Validity" and "entailment" are different ways of talking about the same basic logical relation. Which one of the following statements is true:
1. An argument is valid if and only if the premises entail the conclusion.
2. An argument is valid if and only if the conclusion entails the premises.
3. An argument is valid if and only if the premises and the conclusion entail each other.
4. An argument is valid if and only if either the premises entail the conclusion or the conclusion entails the premises.
Which of the following is NOT an appropriate way to think about entailment?
1. If formula "a" entails formula "b" it means that you could construct a proof from "a" to "b."
2. If formula "a" entails formula "b" then "a" and "b" must be logically equivalent.
3. If formula "a" entails formula "b" then on a table there will be no row on which "a" is true and "b" is false.
4. If formula "a" entails formula "b" then an argument with "a" as its only premise and "b" as its conclusion would be valid.
Which one of the following is NOT a true statement about the relation between logical equivalence and entailment?
1. Two formulas are logically equivalent if and only if they entail each other.
2. If two formulas, p and q, are not equivalent, then neither formula entails the other.
3. Mutual entailment equals logical equivalence.
4. If two formulas, p and q, do not entail each other, then they cannot be logically equivalent.
If formula 'a' entails formula 'b', then on a table:
1. There is no row on which 'a' is true and 'b' is false.
2. There is no row on which 'b' is true and 'a' is false.
3. There is at least one row on which 'a' is true and 'b' is false.
4. There is at least one row on which 'b' is true and 'a' is false.
"Validity" and "entailment" are different ways of talking about the same basic logical relation. Which of the following is true:
1. An argument is valid if and only if the premises entail the conclusion.
2. An argument is valid if and only if the conclusion entails the premises.
3. An argument is valid if and only if the premises and the conclusion entail each other.
4. An argument is valid if and only if either the premises entail the conclusion or the conclusion entails the premises.
Which of the following statements is true. (Only one is true.)
1. Tautologies entail all other formulas.
2. Tautologies are entailed by all other formulas.
3. Contradictions are entailed by all other formuals.
4. Contingencies entail all other formuals.
Which of the following statements is true. (Only one is true.)
1. Contingencies are entailed by all other formulas.
2. Contingencies entail all other formulas.
3. Contradictions are entailed by all other formulas.
4. Contradictions entail all other formulas.
Which of the following statements is true. (Only one is true.)
1. Contingencies are only entailed by other contingencies.
2. Contradictions are only entailed by other contradictions.
3. Tautologies are only entailed by other tautologies.
4. Dessert is only entailed by jello.
Which of the following statements is true. (Only one is true.)
1. Contradictions are entailed by all other formuals.
2. Contradictions only entail other contradictions.
3. Tautologies only entail other tautologies.
4. Tautologies entail all other formulas.
According to the table, which formulas (if any) are logically entailed by M&N?
Choose all correct answers.
1. MvN
2. Mv~M
3. ~N→~N
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by MvN?
Choose all correct answers.
1. M&N
2. Mv~M
3. ~N→~N
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by Mv~M?
Choose all correct answers.
1. M&N
2. MvN
3. ~N→~N
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by ~R&~S?
Choose all correct answers.
1. ~(RvS)
2. ~(R↔R)
3. Sv~S
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by ~(R↔R)?
Choose all correct answers.
1. ~R&~S
2. ~(RvS)
3. Sv~S
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by Sv~S?
Choose all correct answers.
1. ~R&~S
2. ~(RvS)
3. ~(R↔R)
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by ~D→~E?
Choose all correct answers.
1. E→D
2. D→E
3. ~DvE
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by E→D?
Choose all correct answers.
1. ~D→~E
2. D→E
3. ~DvE
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by D→E?
Choose all correct answers.
1. ~D→~E
2. E→D
3. ~DvE
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by A→(B→C)?
Choose all correct answers.
1. (A&B)→C
2. A→(B&C)
3. (A&B)&C
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by A→(B&C)?
Choose all correct answers.
1. A→(B→C)
2. (A&B)→C
3. (A&B)&C
4. None of the formulas are entailed.
According to the table, which formulas (if any) are logically entailed by (A&B)&C?
Choose all correct answers.
1. A→(B→C)
2. (A&B)→C
3. A→(B&C)
4. None of the formulas are entailed.