Q: Are the sum of two periodic functions always periodic?

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Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.

The sum of two odd numbers is always even.

No, the sum of two vectors cannot be a scalar.

Yes the sum of two integers will always be an integer.

The sum of two odd primes is always an even answer or number.

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Yes. You would have to multiply to change it.

Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.

The sum of two odd numbers is always even.

No, the sum of two vectors cannot be a scalar.

No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.

No. While the sum of two qudratics cannot have a power greater than two, it could have a power of 2, 1 or 0. x2 + 1 is one quadratic (2-x)(2+x) is another quadratic. Their sum is 1, a constant (power = 0).

Yes the sum of two integers will always be an integer.

Such a sum is always rational.

Yes, by definition, the sum of two integers is always an integer. Likewise, the product and difference of two integers is always an integer.

the sum of two negative integers is ALWAYS negative

Yes.

The sum of two even numbers is always an even number.