Question

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

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

Which one of the following is a true statement?
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.
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 and the conclusion B is false, then "A implies B" ought to be false.
In the implication "A implies B", if the hypothesis A is false, then we say that the implication "A implies B" is vacuously false.
All of the given statements are false.

Added by Erin B.

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