geometry (please explain)

Question

What is the inverse of the following statement?

"If two lines do not intersect, then the two lines are parallel lines."

A.  If the two lines intersect, then the two lines are not parallel. 

B. If the two lines are not parallel, then the two lines intersect.

 C. If the two lines do not intersect, then the two lines are parallel.

D.  If the two lines are parallel, then the two lines do not intersect.

Answer 1

Given a statement if P then Q

the inverse is if the negation of P, then the negation of Q

the inverse is if not P, then not Q

so A is correct

in this specific example, the given statement is true and the inverse is also true

but that is not always the case. It just happened to be true in this example

if the original statement is if Not P, then Q

then the inverse is if Not Not P, then Not Q

which is the same as if P then Not Q

a double negation such as Not Not P is equivalent to P

Not Not P = P

be careful to Not confuse the inverse with the converse

if the original statement is: if P then Q

the converse is: if Q, then P

the converse switches the P and Q

the original statement is a condition, if the hypothesis then the conclusion

the converse switches the hypothesis and concltion

the "contrapositive" switches the hypothesis and conclusion of the inverse

if the inverse is if Not P then Not Q

then the contrapositive is if Not Q, then Not P

Answer 2

The inverse of the statement If P then Q is: If not P then not Q.

So, for the given question, the answer is A.