JEE MATHEMATICS MCQ: SET THEORY

1 Easy

1 of 1

Application +4 | -1

A = \left\{ {1,\;2,\;3,\;4,\;5} \right\},\;B = \left\{ {2,\;4,\;6} \right\},\;C = \left\{ {3,\;4,\;6} \right\}

, then

\left( {A \cup B} \right) \cap C

View answer and explanation

Correct option: A

\left\{ {3,{\text{ }}4,{\text{ }}6} \right\}

The correct answer is A ({3, 4, 6}) because it is the intersection of the union of A and B with C.

Solution approach

Correct Answer + Core Reason: {3, 4, 6}. This is the intersection of (A union B) with C.

Step-by-Step Solution:

Step 1: Find $A \cup B$ : $A \cup B = \{1, 2, 3, 4, 5, 6\}$ .

Step 2: Find $(A \cup B) \cap C$ : $(A \cup B) \cap C = \{1, 2, 3, 4, 5, 6\} \cap \{3, 4, 6\} = \{3, 4, 6\}$ .

Step 3: Final Answer: {3, 4, 6}

Why other options are wrong:
- Option B ({1, 2, 3}): This is incorrect. It might be a result of miscalculating the union or intersection.
- Option C ({1, 4, 3}): This is incorrect. It might be a result of miscalculating the union or intersection.
- Option D (None of these): This is incorrect because the correct answer is {3, 4, 6}.

Key Concepts:
- Set theory
- Union of sets
- Intersection of sets

Memory Aids:
- Remember the definitions of union and intersection.

Quick Tips:
- List the elements of each set clearly before performing operations.

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