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,
A If x is not < 30, then x is not <40.
B If x < 40, then x < 30. False Counterexample: x = 37
C If x < 40, then x < 30. True
D If x is not < 30, then x is not <40.
Counterexample : x = 31
The converse of the given conditional statement is:
If x < 40, then x < 30.
The truth value of the converse is False.
A counterexample is x = 37 because it satisfies the condition x < 40 but does not satisfy the condition x < 30.
The converse of the conditional statement "If x < 30, then x is not <40" is "If x < 40, then x < 30."
The truth value of the converse is false. A counterexample for this is when x is 37. In this case, x is less than 40 (37 < 40), but it is not less than 30 (37 is not < 30). Therefore, the converse is false.
The converse of a conditional statement switches the hypothesis and conclusion. So, the converse of "If x < 30, then x is not < 40" is "If x is not < 40, then x is not < 30."
To determine the truth value of the converse, we need to check if the statement holds for all possible values of x.
In option B, the converse states "If x < 40, then x < 30." Let's test this statement with a counterexample: If we let x = 37 (which is less than 40), the statement "x < 30" is false. Therefore, the converse is false.
So, the correct answer is B, and a counterexample for the converse is x = 37.