Even Numberslet a1,a2,a3 are even=a1+a2 is even = closure p.pdf
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The document discusses the properties of even and odd integers in terms of group theory. It demonstrates that even integers satisfy closure, associativity, identity, and inverses, confirming that they form a group. In contrast, odd integers fail closure, indicating that they do not form a group.
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Even Numberslet a1,a2,a3 are even=a1+a2 is even = closure p.pdf
- 1. Even Numbers: let a1,a2,a3 are even => a1+a2 is even => closure property is satisfied a1+(a2+a3) = (a1+a2)+a3 => Associative a1 +0 = a1 => Identity element exists a1-a1 = 0 => inverse exists => even integers set is a group ODD Numbers let a1,a2 be two odd numbers => a1 +a2 is even => NOT closed => Odd integers is not a group Solution Even Numbers: let a1,a2,a3 are even => a1+a2 is even => closure property is satisfied a1+(a2+a3) = (a1+a2)+a3 => Associative a1 +0 = a1 => Identity element exists a1-a1 = 0 => inverse exists => even integers set is a group ODD Numbers let a1,a2 be two odd numbers => a1 +a2 is even => NOT closed
- 2. => Odd integers is not a group