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How would you prove that the sum of an even number and an odd number is always an odd number?
Suppose x is an even number and y is an odd number.
Then x = 2*n for some integer n
and y = 2*m + 1 for some integer m
Therefore x + y = 2*n + 2*m + 1 = 2*(n + m) +1
Now, since n and m are integers, (n + m) is also an integer [by the closure of integers under addition].
Thus, x + y = 2*p + 1 where p = n + m is an integer.
ie x + y is an odd integer.
What else can I help you with?
An odd number when squared equals to an even number?
An odd number squared would always equal an odd number and an even number squared would always equal an even
Prove that total number of people who lived on earth and made odd number of handshakes is always even?
If you multiply anything by 2 it always comes out even. So if people make 35 handshakes, we multiply it by 2 and we get 70 people. This will work with any different number of handshakes, odd or even.
Why are square numbers one less than a prime number always even?
Prime numbers, except 2, are always odd (they would not be prime if they were even cos they would be divisible by 2.) 1 less than any odd number must be an even number.
The difference of two even number is always an even number?
Yes, the difference between two even numbers is always an even number.
Is the sum of a prime number and a composite number always even?
No, the sum of a prime number and a composite number is not always even.
How do you use inductive reasoning to prove the product of an odd integer and an even integer will always be even?
The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.
An odd number when squared equals to an even number?
An odd number squared would always equal an odd number and an even number squared would always equal an even
Is an even number plus an even number always even?
Yes, an even number plus an even number is always even. Also, and odd number plus an odd number is always even.
Prove that total number of people who lived on earth and made odd number of handshakes is always even?
If you multiply anything by 2 it always comes out even. So if people make 35 handshakes, we multiply it by 2 and we get 70 people. This will work with any different number of handshakes, odd or even.
What happens when you add an odd number and an odd number?
Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.
Why are square numbers one less than a prime number always even?
Prime numbers, except 2, are always odd (they would not be prime if they were even cos they would be divisible by 2.) 1 less than any odd number must be an even number.
The difference of two even number is always an even number?
Yes, the difference between two even numbers is always an even number.
6 is an even number prove it?
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. 6 is an even number.
Can you prove he hit your car from the damage?
It depends on what angle your car is damaged from. There is always a way to prove everything, even if there is no proof for it.
Is the sum of a prime number and a composite number always even?
No, the sum of a prime number and a composite number is not always even.
What even number and odd number equal a even number?
Your question is incomplete. Adding an even number with an odd number will always result in an odd number. Multiplying an even number with an odd number will always result in an even number.
Is an even number times an even number always even?
yes it is
