Given T = { even numbers from 1 to 12 } N = {common factors of 6, 8 and 12} Find T ∩ N

To solve this problem, we need to break it down into two parts: identifying the elements of set T and set N, and then finding their intersection.

1. Analyze the sets

• Set T (Even numbers from 1 to 12): Even numbers are integers divisible by 2. Between 1 and 12 (inclusive), these are: T = {2, 4, 6, 8, 10, 12}

• Set N (Common factors of 6, 8, and 12): A common factor is a number that divides into all three numbers without leaving a remainder. • Factors of 6: {1, 2, 3, 6} • Factors of 8: {1, 2, 4, 8} • Factors of 12: {1, 2, 3, 4, 6, 12}

Looking at these lists, the numbers that appear in all three are 1 and 2. N = {1, 2}

2. Find the Intersection (T ∩ N)

The intersection (∩) of two sets consists of all elements that are present in both sets.

• T = {2, 4, 6, 8, 10, 12}
• N = {1, 2}

Comparing the two, the only element they share is 2. Therefore, T ∩ N = {2}

3. Conclusion

Comparing our result with the given options: A. {2, 3} B. {2, 3, 4} C. {3, 4, 6} D. {2}

The calculated result matches option D.

Exam Tip: When dealing with "common factors," always list the factors of the smallest number first. This often narrows down your search quickly, as a common factor cannot be larger than the smallest number in the set.