Final answer:
When n is divisible by 12 it's also divisible by 3, as 12 is a multiple of 3. If m is 2 more than a multiple of 6, it is also even, as adding 2 to an even number results in another even number. Finally, if n is an even integer, 3n+5 is odd, as adding 5 to an even number results in an odd number.
Step-by-step explanation:
1. If a number n is divisible by 12, it means n is a multiple of 12. As 12 is itself a multiple of 3 (as 3 multiplied by 4 gives 12), this means n must also be divisible by 3.
2. If m equals 2 more than a multiple of 6, then m can be represented by the formula 6k+2 where k is any integer value. Because 6 is an even number, 6k is always even, and adding 2 to an even number will always result in an even number. Therefore, m is always even.
3. If n is an even integer, this means it can be represented by 2k where k is any integer. Therefore, 3n + 5 can be written as 3(2k)+5, which simplifies down to 6k+5. As 6k is always even, the operation of adding 5 to any even number will result in an odd number. Thus, 3n + 5 is an odd number.
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