Of course not! For example 3 and 9 are odd, but are not co-prime!
yes
Yes, there is exactly one even number between every pair of consecutive odd numbers; I hope that is what the typing-challenged questioner meant.
The parity rules are: Odd + Odd = Even Even + Even = Even Odd + Even = Odd Even + Odd = Odd So the parity where one number is even is that of the other number. This means that you can go through a list of numbers and ignore all the even numbers. Every PAIR of odd numbers has even parity and by the previous paragraph, even parity can be ignored. So you can pair off odd numbers and ignore them.
Any two odd numbers will have an odd product and an even sum.
All the other prime numbers are odd. Every other pair of odd numbers has at least one even number between them. Even numbers greater than two are not prime.
Any pair of one even and one odd number will have an even product and an odd sum.
There are the same amount. Comparing is a bit tricky when there are infinite numbers or both even and odd numbers, but think of it this way: Pair each odd number with the even number right above it (1 & 2, 3 & 4, etc.). Every odd number is paired with one even number, and every even is paired with one odd number. This shows that they have the same amount.
You cannot. There are seven numbers and you cannot pair an odd number of values.
23-13 = 10
There is an even number before and after every odd number and vice versa.
The only way to get an odd product when multiplying two whole numbers is when both of them are odd. Thus, in your example, the only way is by choosing the odd numbers 7 and 5, whose product is 35.
Even numbers must have 2 amongst their factors; they may have other even numbers amongst their factors. Odd numbers must not; every factor of an odd number must be odd.