Question

Which of the following statements is the converse of the “ if the moon is full then the vampires are prowling”.
A.If the vampires are prowling, then the moon is full.
B.If the moon is not full, then the vampires are not prowling.
C.If the vampires are not prowling, then the moon is not full.
D.None.

Answer 1

Hint: This question is from types of statements. There are various logical statements in mathematics. There are certain conditions that decide the type of statement. So if we know the condition then we can easily decide the answer. For the statement to be converse we just interchange the position of hypothesis and conclusion.

Complete step by step solution:
Given the statement is, “ if the moon is full ,then the vampires are prowling”.
Now the part of the statement before then and after is the hypothesis. And the remaining part is the conclusion.
Now for a statement to be converse we will just interchange the positions of the hypothesis and the conclusion.
Here the hypothesis is “ if the moon is full” and the conclusion is “then the vampires are prowling”
Now for the converse statement we will change the position and the structure will be:
 “ if+ conclusion +then +hypothesis”.
So the answer is:
“if the vampires are prowling, then the moon is full”.
So the correct option is A.
So, the correct answer is “Option A”.

Note: We will discuss the remaining two options and their types so that we should know in which type they belong.
Option B:
Here the statements are in their positions only an additional word “not” is used. This is a negative word used. This type of construction is called an “inverse” statement.
“if+ negation of hypothesis then + negation of conclusion”= inverse statement.
Inverse statement is just the negation of the original.
Option C:
Here the statements are interchanged their positions only an additional word “not” is used. This is a negative word used. This type of construction is called a “contrapositive” statement.
“if+ negation of conclusion then + negation of hypothesis”= contrapositive statement.
So we can easily conclude the difference between the types. Hope this helps!