Question

Selecting all the correct answers. Which represents the inverse of this statement? Is the inverse true or false?

Answer 1

Given: A statement- A number is negative if and only if it is less than 0.

p: A number is negative.

q: A number is less than 0.

Required: To find the inverse of the given statement and state if it is true or false.

Explanation: The inverse of the statement will be-

A number is positive if and only if it is greater than 0.

p: A number is positive.

q: A number is greater than 0.

The statement is always true since a positive number is always greater than 0.

Now p and q both are true since any positive number is greater than 0 and any number greater than 0 is always a positive number.

Hence we can write

$\text{\textasciitilde}p\leftrightarrow\text{\textasciitilde}q\text{ }$

The inverse of the given statement is true.

Final Answer: Option D and Option F are correct.