COMEDK · Maths · 20. Sets and Relations

Set \(A=\{x: x\) is a prime number less than 4\(\}\)
\(B=\left\{x: x^2-7 x-18=0, x \in R\right\}\)

Then set \(A\) and \(B\) are

A Equal
B Empty
C Equivalent
D Infinite

Verified Solution

Answer & Solution

Correct Answer

(C) Equivalent

Step-by-step Solution

Detailed explanation

The set \(A\) consists of prime numbers less than 4. The prime numbers less than 4 are 2 and 3. Thus, \(A = \{2, 3\}\). The set \(B\) consists of the roots of the quadratic equation \(x^2 - 7x - 18 = 0\). Factoring the equation, we get \((x - 9)(x + 2) = 0\). Thus, the roots are…

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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Set \(A=\{x: x\) is a prime number less than 4\(\}\)\(B=\left\{x: x^2-7 x-18=0, x \in R\right\}\)Then set \(A\) and \(B\) are

Step-by-step Solution

Set \(A=\{x: x\) is a prime number less than 4\(\}\)
\(B=\left\{x: x^2-7 x-18=0, x \in R\right\}\)

Then set \(A\) and \(B\) are