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  • Write the following sets in the roaster form: (i) A = {x : x ∈ R, 2x + 11 = 15} (ii) B = {x | x2 = x, x ∈ R} (iii) C = {x | x is a positive factor of a prime number p}

Write the following sets in the roaster form:

  1.  A = \{x : x \in R,\ 2x + 11 = 15\}
  2.  B = \{x : x^2 = x, x\in R\}
  3. C = \{x : x\text{ is a positive factor of a prime number }p\}

Answers (1)

(i)    Given that:  A = \{x : x \in R,\ 2x + 11 = 15\}

        \begin{aligned}2x + 11 &= 15 \\ 2x & = 4 \\ x & = 2\end{aligned}

        Hence, A = \{2\}

(ii)    Given that B = \{x : x^2 = x, x\in R\}

        \begin{aligned}x^2 &= x \\ x^2 - x& = 0 \\ x(x-1)&=0 \\ \therefore x =0 & \ x = 1 \end{aligned}

    Hence, B = \{0,1\}

(iii)    Given that C = \{x : x\text{ is a positive factor of a prime number }p\}

        So the positive factors of prime number p are 1 and p. Hence C = \{1,p\}

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