No, some bacteria and other unicellular organisms have a single chromosome
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A diploid number means there are two of every kind of chromosome. For example, humans have 2 sets of 23 chromosomes for a total of 46. Two times any number results in an even number.
Yes, an even number plus an even number is always even. Also, and odd number plus an odd number is always even.
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.
The square of an even number is always even.
The sum of an odd and even number is always odd because there's always one left over. Think of any odd number as being any even number plus one. If you add two even numbers, the answer is always even. If you add an even and an odd (plus one), the answer is always odd.