Pairs of equal sets, if any, give reasons: A = { 0} , B = { x:x, > ,15 and x,

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1.Set Theory

medium

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\,\} $

Option A

Option B

Option C

Option D

Solution

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 $E .$

Standard 11

Mathematics

Write down all the subsets of the following sets

$\{ 1,2,3\} $

easy

For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

hard

(KVPY-2013)

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\} \subset A$

easy

Which of the following are sets ? Justify your answer.

The collection of all natural numbers less than $100 .$

easy

In the following state whether $\mathrm{A = B}$ or not :

$A = \{ x:x$ is a multiple of $10\} ;B = \{ 10,15,20,25,30 \ldots \ldots \} $

easy

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\,\} $

Solution

Similar Questions

Write down all the subsets of the following sets $\{ 1,2,3\} $

For an integer $n$ let $S_n=\{n+1, n+2, \ldots \ldots, n+18\}$. Which of the following is true for all $n \geq 10$ ?

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ? $\{ 3,4\} \subset A$

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In the following state whether $\mathrm{A = B}$ or not : $A = \{ x:x$ is a multiple of $10\} ;B = \{ 10,15,20,25,30 \ldots \ldots \} $

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$A = \{ 0\} ,$

$B = \{ x:x\, > \,15$ and $x\, < \,5\} $

$C = \{ x:x - 5 = 0\} ,$

$D = \left\{ {x:{x^2} = 25} \right\}$

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$\{ 1,2,3\} $

Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?

$\{ 3,4\} \subset A$

Which of the following are sets ? Justify your answer.

The collection of all natural numbers less than $100 .$

In the following state whether $\mathrm{A = B}$ or not :

$A = \{ x:x$ is a multiple of $10\} ;B = \{ 10,15,20,25,30 \ldots \ldots \} $