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COMEDK2025MathematicsSets and RelationsActual

Set A= x: x is a prime number less than 4 B= x: x^2-7 x-18=0, x R Then set A and B are

Options

  1. AEqual
  2. BEmpty
  3. CEquivalent
  4. DInfinite

Correct answer

C. Equivalent

Step-by-step solution

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 x = 9 and x = -2 . So, B = 9, -2 . Comparing the sets, A = 2, 3 and B = 9, -2 . The number of elements in both sets is 2. Since the number of elements in A is equal to the number of elements in B , the sets are equivalent. Answer: Equivalent

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