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Decide, among the following sets, which ...


Decide, among the following sets, which sets are subsets of one and another:
A = { `x : x in R` and x satisfy `x^2 – 8x + 12 = 0` }, B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }.

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To determine which sets are subsets of one another among the given sets A, B, C, and D, we will first express set A in roster form and then analyze the relationships between the sets. ### Step 1: Determine the elements of set A Set A is defined as: \[ A = \{ x : x \in \mathbb{R} \text{ and } x^2 - 8x + 12 = 0 \} \] To find the elements of set A, we need to solve the quadratic equation: \[ x^2 - 8x + 12 = 0 \] ...
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Knowledge Check

  • The set of values of x which satisfy 5x+2 lt 3x +8 and (x+2)/(x-1) lt 4 is

    A
    `(2, 3)`
    B
    `(-oo, 1) cup (2, 3)`
    C
    `(-oo, 1)`
    D
    `(1, 3)`
  • The set of real values of x satisfying the inequality |x^(2) + x -6| lt 6 , is

    A
    `(-4, 3)`
    B
    `(-3, 2)`
    C
    `(-4, -3)cup(2, 3)`
    D
    `(-4, -1) cup (0, 3)`
  • Which of the following is to be added to make x^(6) -6x^(4) + 4x^(3) + 8x^(2) - 10x + 3 a perfect square ?

    A
    `(x -1)^(2)`
    B
    `(x -2)^(2)`
    C
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    D
    `(2x + 1)^(2)`
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