Write Negations for Each of the Following Statements:
(A) $n$

question 9

Essay

Write negations for each of the following statements:
(a) For all integers $n$ , if $n$ is prime then $n$ is odd.
(b) $\forall$ real numbers $x$ , if $x < 1$ then $\frac { 1 } { x } > 1$ .
(c) For all integers $a$ and $b$ , if $a ^ { 2 }$ divides $b ^ { 2 }$ then $a$ divides $b$ .
(d) $\forall$ real numbers $x$ , if $x ( x - 2 ) > 0$ then $x > 2$ or $x < 0$ .
(e) $\forall$ real numbers $x$ , if $x ( x - 2 ) \leq 0$ then $0 \leq x \leq 2$ .
(f) For all real numbers $x$ and $y$ with $x < y$ , there exists an integer $n$ such that $x \leq n \leq y$ .

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Definitions:

Immune System

The body's defense mechanism against pathogens, including various cells, tissues, and organs that fight infections and diseases.

Antigens

Substances that the body recognizes as foreign and that elicit an immune response, often found on the surface of pathogens like bacteria and viruses.

Glucose

A basic form of sugar that serves as a significant source of energy for living beings and is found in numerous carbohydrates.

Red Blood Cells

Cells in the bloodstream that carry oxygen from the lungs to the body's tissues and return carbon dioxide from the tissues back to the lungs.