I need to negate (move the negation inside) or write the contrapositive statements of the following statements:
Write the contrapositive of: If everyone is here, then someone will leave.
Write the negation of: If Alice and Bob go, then Carol or Dave will come.
Write the negation of Every integer is even or odd, but no integer is even and odd.
rewrite as if then statement, then write its contrapositive: Every integer bigger than $1$ is divisible by some prime.
rewrite as if then statement, then negate statement: Every Integer that is divisible by $2$ and $3$ is divisible by $6$.
This is what I’ve done:
If someone didn’t leave, then not everyone was here.
Alice and Bob went; however, neither Carol or Dave came along.
There is an integer that is neither even or odd, or there is an integer that is even or odd.
If $x$ is an integer bigger than $1$, then it is divisble by some prime. Negation: $x$ is an integer bigger than $1$, however $x$ is not divisible by any prime.
If $x$ is an integer divisible by $2$ and $3$ then $x$ is also divisible by $6$. contrapositive: If $x$ is an integer not divisible by $6$, then $x$ is not divisble by $2$ and $3$.
These are not entirely correct, so I was hoping you guys would tell me what's wrong with them and how to fix them.