Which conditional has the same truth as its converse?
A. If x=7, then |x|=7
B. If x-17=4, then x=21
The conditional that has the same truth as its converse is option A: If x=7, then |x|=7. The converse of this statement is: If |x|=7, then x=7. Both statements are true because the absolute value of 7 is indeed equal to 7.
The conditional statement that has the same truth as its converse is option A: "If x=7, then |x|=7."
To determine which conditional statement has the same truth as its converse, we need to evaluate the truth of both the conditional statement and its converse.
A conditional statement has the following form: "If p, then q" where p is the hypothesis (the "if" part) and q is the conclusion (the "then" part).
Converse of a conditional statement is formed by switching the hypothesis and the conclusion: "If q, then p".
Let's evaluate the truth of both conditional statement A and its converse:
A. If x = 7, then |x| = 7.
Converse of A: If |x| = 7, then x = 7.
To test the truth of these statements, we need to consider different values of x.
If we substitute x = 7 into A, it becomes "If 7 = 7, then |7| = 7". This statement is true because 7 is indeed equal to 7, and the absolute value of 7 is also 7.
Now, let's evaluate the converse of A. If we substitute |x| = 7 into the converse of A, it becomes "If 7 = 7, then x = 7". This statement is also true because if 7 equals 7, then x must also be 7.
Since both the conditional statement A and its converse are true, we can conclude that option A "If x = 7, then |x| = 7" has the same truth as its converse.