Set, Relation and FunctionHard

Question

Let $A = \left\{ x:\left| x^{2} - 10 \right|\ 6 \right\}$ and $B = \{ x:|x - 2| > 1\}$. Then

Options

A.$A \cup B = ( - \infty,1\rbrack \cup (2,\infty)$
B.$A - B = \lbrack 2,3)$
C.$A \cap B = \lbrack - 4, - 2\rbrack \cup \lbrack 3,4\rbrack$
D.$B - A = ( - \infty, - 4) \cup ( - 2,1) \cup (4,\infty)$

Solution

$\left| x^{2} - 10 \right| \leq 6$

$${- 6 \leq x^{2} - 10 \leq 6 }{4 \leq x^{2} \leq 16 }{A = \lbrack - 4, - 2\rbrack \cup \lbrack 2,4\rbrack }{|x - 2| > 1 }{B = ( - \infty,1) \cup (3,\infty) }{A \cup B = ( - \infty,1) \cup \lbrack 2,\infty) }{A \cap B = \lbrack - 4, - 2\rbrack \cup (3,4\rbrack }{A - B = \lbrack 2,3\rbrack }{B - A = ( - \infty, - 4) \cup ( - 2,1) \cup (4,\infty)}$$

Create a free account to view solution

View Solution Free
Topic: Set, Relation and Function·Practice all Set, Relation and Function questions

More Set, Relation and Function Questions

Let f be a real-valued function defined on the interval (0, ∞) by f(x) = ln x + . Then which ofthe following state...If A, B and C are any three sets, then A × (B ∪ C) is -...Let R be a relation defined in the set of real numbers by a R b ⇔ 1 + ab > 0. Then R is-...The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three n...Let a differentiable function f(x) be such that 3|f(x) - f(y)| ≤ 2|x - y| ∀ x, y ∈ R and f′(x) &...