What is the converse of the following conditional statement. Determine the truth value of the converse. If it is false, then provide a counter-example. If x < 30, then x < 40 (1 point)
A If x < 40, then x < 30. True
B If x is not < 30, then x is not <40.
C If x < 40, then x < 30. False Counterexample : x = 37
D If x is not < 30, then x is not <40. Counterexample : x = 31
The converse of the conditional statement "If x < 30, then x < 40" is "If x < 40, then x < 30."
The truth value of the converse is False.
To provide a counterexample, we can use the value x = 37.
If x = 37, then the original statement "If x < 30, then x < 40" is true because 37 < 30 is false, so the whole statement is true.
However, for the converse statement "If x < 40, then x < 30", 37 < 40 is true, but 37 < 30 is false, so the whole statement is false.
The converse of the conditional statement "If x < 30, then x < 40" is "If x < 40, then x < 30."
To determine the truth value of the converse, we can use the counterexample method. A counterexample is a specific example that proves a statement false.
In this case, the converse statement is false.
Counterexample:
Let's take x = 37. According to the original conditional statement, if x < 30, then x < 40. Since 37 is not less than 30, the original statement is true.
However, in the converse statement "If x < 40, then x < 30," if we substitute x = 37, we can see that 37 is indeed less than 40, but it is not less than 30. Therefore, the converse statement is false.
So, the answer is:
D: If x is not < 30, then x is not < 40. (Counterexample: x = 31)
The converse of a conditional statement switches the hypothesis and conclusion.
The original conditional statement is "If x < 30, then x < 40."
The converse of this statement is "If x < 40, then x < 30."
To determine the truth value of the converse, we need to see if the converse is always true or false.
Option A states that the converse is true. However, it is incorrect. A counterexample for option A is x = 37. If we substitute x = 37 into the converse statement, we get "If 37 < 40, then 37 < 30." This is false, as 37 < 30 is not true.
Option B states that " If x is not < 30, then x is not <40." This is the contrapositive of the original statement, not the converse. The contrapositive statement is always true if the original statement is true.
Option C states that the converse is false. This is correct. The counterexample for option C is x = 37. When we substitute x = 37 into the converse statement, we get "If 37 < 40, then 37 < 30." This statement is not true because 37 < 30 is false.
Option D restates option B, which is the contrapositive.
Therefore, the correct answer is C. The converse is false, with the counterexample x = 37.