Answer: No, the set of odd integers is not closed for addition
Step-by-step explanation:
It's asking if we can take any two odd numbers, add them, and get an odd number result.
Here are some counterexamples
3+5 = 8
1+23 = 24
89+11 = 100
All it takes is one pair of odd numbers to add to something not odd to show that the set of odd integers is not closed for addition.
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In contrast, the set of even numbers is closed under addition. We can add any two even numbers to get some even number result
2+4 = 6
8+10 = 18
20+30 = 50
and so on
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The proof is given below
m and n are integers
2m = some even number
2n = some other even number
2m+2n = 2(m+n) = 2*(integer) = another even integer
This proves that adding any two even integers leads to another even integer.