Question

What is the inverse of the statement below?

Answer 1

Answer:

Inverse of f ⇒ g statement is ¬ g ⇒ ¬f.

Step-by-step explanation:

Given f ⇒ g written equivalently f implies g or if f then g.

We have to write the inverse statement for this .

f ⇒ g is a conditional statement which says if  f is true then only g is true.

For inverse statement , we write its converse as :

if g is not true then f is also not true.

Mathematically written as ¬ g ⇒ ¬f.

For example:  “if John is married then he has a spouse”

here, f = john is married.

g = he has a spouse.

that is , f ⇒ g

For inverse , if john do not have a spouse then he is not married.

that is ¬ g ⇒ ¬f.

Answer 2

Answer:  The inverse of  the statement f  ⇒  g is  ~g ⇒  ~f.

Step-by-step explanation:  We are given to find the inverse of the following statement :

f  ⇒  g.

Here, in the given statement, the hypothesis is p and conclusion is q.

We know that

to find the inverse of a conditional statement, we need to negate the hypothesis and conclusion and then change their position.

Therefore, the inverse of f  ⇒  g  will be

not g ⇒  not f

That is, ~g ⇒ ~f.

For example, the inverse of a statement "If it rains, I will go to the roof" is given by

"If I will not go the roof, then it will not rain."

Thus, the inverse of the statement f  ⇒  g is  ~g ⇒  ~f.