write the converse, inverse, and contrapositive of the following statement. if he wants to smile, then he is…

write the converse, inverse, and contrapositive of the following statement. if he wants to smile, then he is mad. the converse of the given statement is which of the following? a. if he is mad, then he wants to smile. b. if he does not want to smile, then he is not mad. c. he does not want to smile or he is mad. d. if he is not mad, then he does not want to smile. the inverse of the given statement is which of the following? a. if he is mad, then he wants to smile. b. he does not want to smile or he is mad. c. if he is not mad, then he does not want to smile. d. if he does not want to smile, then he is not mad.

write the converse, inverse, and contrapositive of the following statement. if he wants to smile, then he is mad. the converse of the given statement is which of the following? a. if he is mad, then he wants to smile. b. if he does not want to smile, then he is not mad. c. he does not want to smile or he is mad. d. if he is not mad, then he does not want to smile. the inverse of the given statement is which of the following? a. if he is mad, then he wants to smile. b. he does not want to smile or he is mad. c. if he is not mad, then he does not want to smile. d. if he does not want to smile, then he is not mad.

Answer

Brief Explanations:

  1. Recall the definitions:
    • The converse of a conditional statement “If (p), then (q)” is “If (q), then (p)”. Here (p =) “he wants to smile” and (q=) “he is mad”. So the converse is “If he is mad, then he wants to smile”.
    • The inverse of a conditional statement “If (p), then (q)” is “If not (p), then not (q)”. So the inverse is “If he does not want to smile, then he is not mad”.

Answer:

The converse: A. If he is mad, then he wants to smile. The inverse: D. If he does not want to smile, then he is not mad.