If X= { a, b, c, d } and Y = { f, b, d, g}, find X ∩ Y. | Mathematics MCQ | Examoogle

MathematicsSet Theory

If X= { a, b, c, d } and Y = { f, b, d, g}, find X ∩ Y.

{ a, c}

{ g, f }

{ a, b, c, d, g, f }

{ b, d }

Correct Answer

📐 MA • Math Direct Set TheoryMathematicsSet Theory

Option D

{ b, d }

Quick Summary:

Scan the first set X and check if each element is present in Y. Mark only those that appear in both lists.

📐MAMath SolutionDirect Set Theory

📋 Given

Two sets are provided: X = { a, b, c, d } and Y = { f, b, d, g }.

🔢 Formula Used

X∩Y={x:x∈X and x∈Y}X \cap Y = \{ x: x \in X \text{ and } x \in Y \}X∩Y={x:x∈X and x∈Y}

⚡ Exam Hall Shortcut / Speed Trick

Scan the first set X and check if each element is present in Y. Mark only those that appear in both lists.

⚠️ Common Student Trap / Pitfall

Confusing the intersection symbol ( $\cap$ , elements common to both) with the union symbol ( $\cup$ , elements present in either set).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify elements of Set X

List all elements present in the first set: $X = \{a, b, c, d\}$ .

X={a,b,c,d}X = \{a, b, c, d\}X={a,b,c,d}

Identify elements of Set Y

List all elements present in the second set: $Y = \{f, b, d, g\}$ .

Y={f,b,d,g}Y = \{f, b, d, g\}Y={f,b,d,g}

Find the intersection

Find elements that exist in both $X$ and $Y$ . Comparing the two, we see that 'b' and 'd' are common to both sets.

X∩Y={b,d}X \cap Y = \{b, d\}X∩Y={b,d}

✅

D is correct because the intersection represents the elements common to both sets, which are {b, d}.

Core Concepts Used

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💡 EXAM TIP

Intersection problems are fundamental for Venn diagram questions in data interpretation and logical reasoning sections.

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