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:

Bondholders

Individuals or entities that hold debt securities issued by corporations or governments, expecting to receive fixed interest payments and the principal back at maturity.

Market Interest Rate

The prevailing rate at which borrowers and lenders agree to transact, not set by any one institution but by market demand and supply.

Contractual Interest Rate

The agreed-upon rate of interest that is to be paid on a loan, as defined in the loan agreement.

Face Value

The nominal value printed on a bond or other financial instrument, independent of its market value.