Question

Which one of the following is a true statement? In the implication "A implies B", if the hypothesis A is true, then "A implies B" ought to be true (regardless of the truth value of B). In the implication "A implies B", if the hypothesis A is false, then we say that the implication "A implies B" is vacuously false. If x is a real number, then "0 ? x and 0 ? x" is always true. The equivalence "A ? B" is true if and only if A and B have the same truth value. All of the given statements are false. In the implication "A implies B", if the hypothesis A is false and the conclusion B is false, then "A implies B" ought to be false.

          Which one of the following is a true statement?

In the implication "A implies B", if the hypothesis A is true, then "A implies B" ought to be true (regardless of the truth value of B).

In the implication "A implies B", if the hypothesis A is false, then we say that the implication "A implies B" is vacuously false.

If x is a real number, then "0 ? x and 0 ? x" is always true.

The equivalence "A ? B" is true if and only if A and B have the same truth value.

All of the given statements are false.

In the implication "A implies B", if the hypothesis A is false and the conclusion B is false, then "A implies B" ought to be false.

Which one of the following is a true statement?

In the implication "A implies B", if the hypothesis A is true, then "A implies B" ought to be true (regardless of the truth value of B).

In the implication "A implies B", if the hypothesis A is false, then we say that the implication "A implies B" is vacuously false.

If x is a real number, then "0 ? x and 0 ? x" is always true.

The equivalence "A ? B" is true if and only if A and B have the same truth value.

All of the given statements are false.

In the implication "A implies B", if the hypothesis A is false and the conclusion B is false, then "A implies B" ought to be false.

Added by Alec K.

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