1. negations

Negate this sentence: If n is prime, then n is odd or n is 2.

I know the purpose is to just to negate the sentence no matter what.

The negation solution is: n is a prime and n is even and n is not 2.

So in discrete math, it doesn't matter if this is really true or not? its just an example???

i don't think its possible to have n be prime, and alos be even at the same time, if its not 2.

thanks for help with this.

2. Hello, rcmango!

Negate this sentence: . $\text{ If }n\text{ is prime, then }n\text{ is odd or }n\text{ is 2.}$

We have: . $(n\text{ prime}) \rightarrow \bigg[(n\text{ odd}) \vee (n = 2)\bigg]$

which is equivalent to: . $\sim\!(n\text{ prime})\; \vee\: (n\text{ odd}) \:\vee\: (n=2)$

The negation is: . $\sim\bigg[\sim\!(n\text{ prime}) \:\vee \n\text{ odd}) \:\vee \n=2)\bigg] " alt="\sim\bigg[\sim\!(n\text{ prime}) \:\vee \n\text{ odd}) \:\vee \n=2)\bigg] " />

. . . . . . . . . . $\Longleftrightarrow\;\;(n\text{ prime)}\; \:\wedge \:\sim\!(n\text{ odd}) \;\wedge \:\sim\!(n = 2)$

. . . . . . . . . . $\Longleftrightarrow\;\;(n\text{ prime})\;\wedge \;(n\text{ even}) \;\wedge\;(n \neq 2)$