COMEDK · Maths · 20. Sets and Relations

If \(A = \{x : x\ \text{is the first three odd numbers}\}\)
\(B = \{2x + 3 : 0 \leq x < 5, x \in \mathbb{N}\}\), then which of the following is true

A \(A \cap B = \emptyset\)
B \(A \cap B\) is a singleton set
C \(A \subset B\)
D \(n(B) = 5\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(A \cap B\) is a singleton set

Step-by-step Solution

Detailed explanation

The first three odd natural numbers are \(1, 3\), and \(5\). \(A = \{1, 3, 5\}\) For set \(B\), the condition is \(0 \leq x < 5\) and \(x \in \mathbb{N}\). The natural numbers satisfying this condition are \(x = 1, 2, 3, 4\). Substituting these values into \(2x + 3\): For…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If \(A = \{x : x\ \text{is the first three odd numbers}\}\)\(B = \{2x + 3 : 0 \leq x < 5, x \in \mathbb{N}\}\), then which of the following is true

Step-by-step Solution

If \(A = \{x : x\ \text{is the first three odd numbers}\}\)
\(B = \{2x + 3 : 0 \leq x < 5, x \in \mathbb{N}\}\), then which of the following is true