To verify the conjecture that the sum of any two odd numbers is even, let’s consider each pair of odd numbers provided and determine their sum step-by-step.
### Pairs of Odd Numbers and Their Sums
1. First pair: [tex]\(1 + 1\)[/tex]
- Both 1 and 1 are odd numbers.
- Their sum is [tex]\(1 + 1 = 2\)[/tex].
2. Second pair: [tex]\(1 + 5\)[/tex]
- Both 1 and 5 are odd numbers.
- Their sum is [tex]\(1 + 5 = 6\)[/tex].
3. Third pair: [tex]\(7 + 9\)[/tex]
- Both 7 and 9 are odd numbers.
- Their sum is [tex]\(7 + 9 = 16\)[/tex].
4. Fourth pair: [tex]\(9 + 11\)[/tex]
- Both 9 and 11 are odd numbers.
- Their sum is [tex]\(9 + 11 = 20\)[/tex].
5. Fifth pair: [tex]\(13 + 21\)[/tex]
- Both 13 and 21 are odd numbers.
- Their sum is [tex]\(13 + 21 = 34\)[/tex].
6. Sixth pair: [tex]\(101 + 103\)[/tex]
- Both 101 and 103 are odd numbers.
- Their sum is [tex]\(101 + 103 = 204\)[/tex].
### Observations
From our calculations:
- [tex]\(1 + 1 = 2\)[/tex]
- [tex]\(1 + 5 = 6\)[/tex]
- [tex]\(7 + 9 = 16\)[/tex]
- [tex]\(9 + 11 = 20\)[/tex]
- [tex]\(13 + 21 = 34\)[/tex]
- [tex]\(101 + 103 = 204\)[/tex]
It can be observed that the sum of two odd numbers results in an even number in all cases. Hence, the conjecture that the sum of any two odd numbers is even seems to be true from our given examples.
