Find the pairs of equal sets, if any, give reasons:
$A = \{ 0\} ,$
$B = \{ x:x\, > \,15$ and $x\, < \,5\} $
$C = \{ x:x - 5 = 0\} ,$
$D = \left\{ {x:{x^2} = 25} \right\}$
$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $
Find the pairs of equal sets, if any, give reasons:
$A = \{ 0\} ,$
$B = \{ x:x\, > \,15$ and $x\, < \,5\} $
$C = \{ x:x - 5 = 0\} ,$
$D = \left\{ {x:{x^2} = 25} \right\}$
$E = \{ \,x:x$ is an integral positive root of the equation ${x^2} - 2x - 15 = 0\,\} $
Since $0 \in A$ and $0$ does not belong to any of the sets $B, C, D$ and $E,$ it follows that, $A \neq B, A \neq C, A \neq D, A \neq E.$
Since $B =\phi$ but none of the other sets are empty. Therefore $B \neq C , B \neq D$ and $B \neq E$. Also $C =\{5\}$ but $-5 \in D$, hence $C \neq D$.
Since $E =\{5\}, C = E .$ Further, $D =\{-5,5\}$ and $E =\{5\},$ we find that, $D \neq E$
Thus, the only pair of equal sets is $C$ and $E .$
Similar Questions
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ 3,4\} \in A$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{ 3,4\} \in A$
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
- [KVPY 2012]
Which of the following are sets ? Justify your answer.
The collection of questions in this chapter.
Which of the following are sets ? Justify your answer.
The collection of questions in this chapter.
Write the following as intervals :
$\{ x:x \in R,0\, \le \,x\, < \,7\} $
Write the following as intervals :
$\{ x:x \in R,0\, \le \,x\, < \,7\} $
In rule method the null set is represented by
In rule method the null set is represented by