What is the contrapositive assumption of the following statement?

If [tex]x^5 + 7x^3 + 5x \geq x^4 + x^2 + 8[/tex], then [tex]x^3 - x < 5[/tex].

A. If [tex]x^3 - x \geq 5[/tex], then [tex]x^5 + 7x^3 + 5x \geq x^4 + x^2 + 8[/tex].

B. If [tex]x^3 - x \geq 5[/tex], then [tex]x^5 + 7x^3 + 5x \geq x^4 + x^2 + 8[/tex].

C. If [tex]x^3 - x \geq 5[/tex], then [tex]x^5 + 7x^3 + 5x < x^4 + x^2 + 8[/tex].

D. If [tex]x^5 + 7x^3 + 5x < x^4 + x^2 + 8[/tex], then [tex]x^3 - x \geq 5[/tex].

E. If [tex]x^5 + 7x^3 + 5x \geq x^4 + x^2 + 8[/tex], then [tex]x^3 - x > 5[/tex].

The contrapositive assumption of the given statement is:If [tex]x^3 - x < 5[/tex]then [tex]x^5 + 7x^3 + 5x < x^4 + x^2 + 8[/tex].Therefore, the answer is option c).

The contrapositive statement of a conditional statement is formed by negating both the hypothesis and conclusion of the conditional statement and reversing them. It is logically equivalent to the original statement.

Let's take a look at how we can arrive at the contrapositive of the given statement.If [tex]x^5 + 7x^3 + 5x ≥ x^4 + x^2 + 8[/tex], then [tex]x^3 - x < 5.[/tex]

Now let us negate both the hypothesis and conclusion of the conditional statement to get its contrapositive assumption which is:If[tex]x^3 - x < 5[/tex] then[tex]x^5 + 7x^3 + 5x < x^4 + x^2 + 8.[/tex]

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