Given that A = {3, 4, 1, 10, ⅓ } B = {4, 3,⅓, ⅓, 7}. Find A∩B

1. Analyze the question

The question asks for the intersection of two sets, $A$ and $B$. In set theory, the intersection of two sets (denoted as $A \cap B$) consists of all elements that are present in both set $A$ and set $B$.

2. Explain the concept

• Set A: $\{3, 4, 1, 10, \frac{1}{3}\}$
• Set B: $\{4, 3, \frac{1}{3}, \frac{1}{3}, 7\}$
• Intersection ($A \cap B$): You look for common members. Note that in set theory, duplicate elements within a single set are usually written once (e.g., $\{ \frac{1}{3}, \frac{1}{3} \}$ is the same as $\{ \frac{1}{3} \}$).

3. Show the solution

• Step 1: List the elements of Set A: $3, 4, 1, 10, \frac{1}{3}$
• Step 2: List the elements of Set B: $4, 3, \frac{1}{3}, 7$ (we simplify the duplicate $\frac{1}{3}$)
• Step 3: Compare the two sets to find common elements: • Is 3 in both? Yes. • Is 4 in both? Yes. • Is 1 in both? No (it is only in A). • Is 10 in both? No (it is only in A). • Is $\frac{1}{3}$ in both? Yes. • Is 7 in both? No (it is only in B).

• Step 4: Combine the common elements: $\{3, 4, \frac{1}{3}\}$

4. Identify the answer

Comparing our result $\{3, 4, \frac{1}{3}\}$ to the given options, it matches Option C.

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5. Tip

When dealing with set intersection questions in JAMB, always write out the sets clearly and cross out elements that do not appear in both lists. Don't be distracted by extra numbers or duplicates; focus only on the "shared" values!