Tag: introduction to set

Questions Related to introduction to set

State True or False
$\displaystyle \phi \cap A=A$

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. True

  2. False

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Correct Option: B
Explanation:

True as $\displaystyle \phi'\cap A=U\cap A=A$

In a group of $500$ people $200$ can speck Hindi alone while only $125$ can speck English alone The number of people can speck both Hindi and English is

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $175$

  2. $325$

  3. $300$

  4. $375$

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Correct Option: A
Explanation:

Total no. of people$=500$

People who speak Hindi only$=200$
People who speak English only$=125$
$\therefore$ The number of people who can speak both Hindi and English$=500-(200+125)$
$\Rightarrow 500-325=175$

Given $A={a,b,c,d,e,f,g,h}$ and $B={a,e,i,o,u}$ then $A\cap B$ is equal to

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. ${a,e}$

  2. ${f,g}$

  3. ${g,h}$

  4. ${i,u}$

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Correct Option: A
Explanation:
Given, $A=\{a,b,c,d,e,f,g,h\}$ and $B=\{a,e,i,o,u\}$

$ A$ intersection $B $, which means a new set can be constructed by determining which members are common among the two sets.

So as per the question:-
$A\cap B=\left\{ a,e \right\}$

If X=(multiples of $2$ ), Y = ( multiples of $5$) , Z= (multiples of $10$), then $ \displaystyle X \cap(Y\cap Z)    $ is equal to 

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. Multiples of $10$

  2. Multiples of $5$

  3. Multiples of $2$

  4. Multiples of $7$

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Correct Option: A
Explanation:
$x= (multiples\ of\ 2\ is\ 2, 4, 6, 8, 10.............)$
$y=(multiples\ of\ 5\ is\ 5, 10,15,20,25.........)$
$z=(multiples\ of\ 10\ is\ 10,20,30,40...........)$
Then, $ X\cap(Y\cap Z)$

Apply the value
$=(2, 4, 6, 8, 10,.......)\cap[ (5, 10, 15, 20, 25,........)\cap (10, 20, 30, 40,.......)]$
$=(2, 4, 6, 8, 10,.......)\cap (10, 20, 30,........)$
$=(10, 20, 30,........)$

Hence, this is multiple of $10$.


Hence, this is the answer.

If $A={x:x^2-3x+2=0}$ and $B={x:x^2+4x-5=0}$ then the value of $A-B$ is

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. ${1,2}$

  2. ${2}$

  3. ${1}$

  4. ${5,2}$

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Correct Option: B
Explanation:

$A={x:x^2-3x+2=0}\implies A={1,2}$
$B={x:x^2+4x-5=0}\implies A={1,-5}$
$\therefore A-B={2}$

There are $19$ hockey players in a club. On a particular day $14$ were wearing the prescribed hockey shirts, while $11$ were wearing the prescribed hockey pants. None of them was without hockey pant or hockey shirt. How many of them were in complete hockey uniform?

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $8$

  2. $6$

  3. $9$

  4. $7$

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Correct Option: B
Explanation:

$n(S\cup P) = 19$

$n(S)=14 $
$ n(P)= 11 $
$n(S\cup P)= n(S)+n(P)-n(S\cap P)$
$19=14+11-n(S\cap P)$
$n(S\cap P)= 25-19 = 6$

Out of $450$ students in a school, $193$ students read Science Today, $200$ students read Junior Statesman, while $80$ students read neither. How many students read both the magazines?

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $137$

  2. $80$

  3. $57$

  4. $23$

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Correct Option: D
Explanation:

$n(U)=450$

n(Students read Science Today) $=193 =n(S) $

n(Students read Junior Statesman) $=200=n(J) $

n(students read neither) $=80$

$n(S \cup J) $= n(U)-n(students read neither) $= 450-80=370$

Also, $n(S \cup J) = n(S) + n(J)-n(S\cap J) $

$370 = 193+200-n(S\cap J) $

$n(S\cap J)=393-370 =23 $

In a community of $175$ persons, $40$ read the Times, $50$ reads the Samachar and $100$ do not read any. How many persons read both the papers?

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $10$

  2. $15$

  3. $20$

  4. $25$

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Correct Option: B
Explanation:

$n(U)=175$

n(read Times) $=40 =n(T) $

n(read the samachar) $=50 = n(S) $

n(do not read any) $= 100$

$n(T\cup S)=  n(U)-$ n(do not read any) $= 175-100 =75$

$\therefore n(T \cup S)= n(T)+ n(S)- n(T\cap S) $

$n(T\cap S) =90-75 =15$

In a group of $15, 7$ have studied, German, $8$ have studied French, and $3$ have not studied either. How many of these have studied both German and French?

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $0$

  2. $3$

  3. $4$

  4. $5$

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Correct Option: B
Explanation:

$n(U)=15$

$n(German) =7 =n(G) $

$n(French) =8 =n(F) $

n(students who have studied neither) $=3$

$n(G \cup F) = n(U)-$ n(students who studied neither) $= 15-3=12 $

$n(G \cup F) = n(G) + n(F)-n(G\cap F) $

$12 = 7+8-n(G\cap F) $

$n(G\cap F)=15-12=3 $

In a class consisting of $100$ students, $20$ know English and $20$ do not know Hindi and $10$ know neither English nor Hindi. The number of students knowing both Hindi and English is

mathematics and statistics introduction to set union and intersections union and intersection of sets basic operations on sets

  1. $5$

  2. $10$

  3. $15$

  4. $20$

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Correct Option: B
Explanation:

$n(U)=100$

$n(English) =20 =n(E) $

$n(Hindi) =100- 20= 80 =n(H) $

n(students who have studied neither Hindi nor English) $=10$

$n(E \cup H) = n(U)-$ n(students who studied neither) $= 100-10 =90 $

$n(E \cup H) = n(E) + n(H)-n(E\cap H) $

$90 = 20+80-n(E\cap H) $

$n(E\cap H)= 10$