Addition of even integers gives even integers and hence it is closed.
Addition of odd integers gives even integers and hence it is not closed.
Multiplication of even integers gives even integers and hence it is closed.
Multiplication of odd integers gives odd integers and hence it is closed.
To see this mathematically you do the following: Assume you have two even numbers i.e. 2k and 2m, for k,m integers. Then 2k+2m=2(k+m)=even. But if you have two odd numbers, lets say 2k+1 and 2m+1 then if you add them (2k+1)+(2m+1)=2k+2m+2=2(k+m+1)=even.
Nikolaos P.
tutor
Division takes you out of the set of integers since for example 1 and 2 are both integers but 1/2=0.5 which is not an integer any more. About subtraction you can try to play with the expressions 2k-2m and (2k+1)-(2m+1). Then you will see that if you subtract even numbers you stay in the even integer set but if you subtract odd numbers you don't stay in the odd integer set.
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10/07/20
Tarita L.
What about subtraction and division10/07/20