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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.

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Q: How could you determine whether a sum of numbers such as 127 plus 38 is even or odd?
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How would you determine whether the product of many natural numbers is even or odd?

If at least one of the numbers is even, the result will be even. Otherwise all the numbers are odd and the result will be odd.


Is the set of prime numbers is well defined or not and why?

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.


Without building a tile model how can you determine whether a sum of numbers is even or odd?

You have to look at the ones place digit for the quick way to this. If both ones digits are even then it will be even, if they are both odd then it will be even, if one is odd and one is even then it will be odd.


Can you tell if sum of several numbers will be even or odd?

Yes, all you have to do is to count the number of ODD numbers in the list. If it is odd, then the sum will be odd; if even, so will the sum. Knowing this can help you run a quick validity check when you sum up a list of numbers. (The method works because: a) the sum of two even numbers is even, and b) the sum pf two odd numbers is even, but c) the sum of an even number and an odd number is odd. Hence, if you only determine whether there are any unpaired odd numbers, you know the answer.)


Is the set of prime numbers well defined?

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.

Related questions

How would you determine whether the product of many natural numbers is even or odd?

If at least one of the numbers is even, the result will be even. Otherwise all the numbers are odd and the result will be odd.


What is the next number 2 7?

It can be any number. Two numbers do not even determine whether the "sequence" is arithmetic, geometric or other.


How can you determine whether a sum of several numbers such as 13 45 24 17 is even or odd?

Add them up and divide the sum by 2.


Is the set of prime numbers well defined or not?

Well, there is a clear definition, and at least in theory you can always determine whether a number is a primer number or not, so I would say, yes.


Is the set of prime numbers is well defined or not and why?

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.


Without building a tile model how can you determine whether a sum of numbers such as 127 38 is even or odd?

None Of Them Equals 100 and 10 so 127 is 130


Without building a tile model how can you determine whether a sum of numbers is even or odd?

You have to look at the ones place digit for the quick way to this. If both ones digits are even then it will be even, if they are both odd then it will be even, if one is odd and one is even then it will be odd.


Can you tell if sum of several numbers will be even or odd?

Yes, all you have to do is to count the number of ODD numbers in the list. If it is odd, then the sum will be odd; if even, so will the sum. Knowing this can help you run a quick validity check when you sum up a list of numbers. (The method works because: a) the sum of two even numbers is even, and b) the sum pf two odd numbers is even, but c) the sum of an even number and an odd number is odd. Hence, if you only determine whether there are any unpaired odd numbers, you know the answer.)


Is the set of prime numbers well defined?

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.


Why are numbers odd and even?

That's a more or less arbitrary name given to numbers, to distinguish whether they are divisible by 2 (even) or not (odd).


Could prime numbers never be even numbers?

The only even prime number is 2.


How can you determine whether a sum of numbers is even or odd with out building a tile model or computing the sum?

You can just add the last digit of each number. Whenever you get a two-digit number, you can discard all digits except the last one. Another alternative is to count how many odd numbers there are - once again, you only need to consider the last digit. If the number of odd numbers is even, the sum is even; otherwise it is odd. (You can ignore even numbers for this calculation.)