Question

The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.” What is the contrapositive of the original conditional statement?

Answer 1

The contrapositive of the original conditional statement is if it has a positive cube root then the number is positive.

Explanation:

In mathematics, a cube root is $y^3 = x$

The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.” It means y is negative, so the cube root of negative will result the negative value. For example: $(-1)^3 = -1$

A conditional statement and its inverse are not logically equivalent

In conditional statements, "If p then q" is denoted symbolically by "p q"; p is called the hypothesis and q is called the conclusion. Suppose we give a conditional statement of the form "If p then q", then  the inverse is "If ~p then ~q." Symbolically, the inverse of p q is ~p ~q

The original conditional statement is If a number is positive, then it has a positive cube root

What is the contrapositive of the original conditional statement?  The contrapositive of a conditional statement of the form "If p then q" is  "If  ~q then  ~p". Then the answer could be if it has a positive cube root then the number is positive.

Learn more about the inverse of function at: brainly.com/question/10250188

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Answer 2

Answer:

If a number does not have a negative cube root, then the number is not negative .

Step-by-step explanation:

"If a number is negative, then it has a negative cube root" has the form:

p -> q

where p is "a number is negative" and q is "a number has a negative cube root".

Then, the contrapositive of the original conditional statement must be:

¬q -> ¬p

where ¬q is " a number does not have a negative cube root" and ¬p is "a number is not negative".