If  X = {x : x < 7} and Y = {y:y is a factor of 24} are subsets of $\mu$ = {1, 2, 3...10} find X $\cap$ Y.

Step 1: Analyze the question We need the elements common to X and Y, where both sets are subsets of the universal set μ = {1, 2, 3, ..., 10}.

Step 2: List the sets

• X = {x : x < 7} within μ gives X = {1, 2, 3, 4, 5, 6}
• Y = {factors of 24} within μ. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Only those in μ are kept, so Y = {1, 2, 3, 4, 6, 8}

Step 3: Find the intersection (X ∩ Y) The intersection contains the elements that appear in both sets:

• 1 is in both
• 2 is in both
• 3 is in both
• 4 is in both
• 5 is in X only (5 does not divide 24)
• 6 is in both
• 8 is in Y only (8 is not less than 7)

So X ∩ Y = {1, 2, 3, 4, 6}

Answer: Option B.

Tip: When a question gives a universal set, first list each set explicitly. Then check each element one at a time. Don't forget that 1 is a factor of every number, which is a common mistake in options like A and C.