EASY
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Important Questions on Theory of Sets

EASY
In a class, students are assigned roll numbers from I to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of students who did not opt for any of the three sports is
MEDIUM
Prove that A-BC=A-BA-C by using Venn diagrams.
EASY

In the given Venn diagram nA is

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EASY
Write A=2, 4, 8, 16 in set-builder form.
MEDIUM
An investigator interviewed 100 students to determine the performance of three drinks milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee, 30 students take coffee and tea, 25 students take milk and tea, 12 students take milk only, 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of the three drinks is
MEDIUM
If A={x:x is a letter of the word EXAMINATION}, then its roster form is 
MEDIUM
Which of the following statements is false?
MEDIUM

If 

A=x:x is a natural number less than is 6

B=x:x is a pime number which is a divisor of 60

C=x:x is an odd natural number less than 10

D=x:x is an even natural number which is a divisor of 48

Then write roster form for all above sets and find AB

MEDIUM
If A=a1, a2, .a10: a1{1, 2, 3}, a1+ai+1 is even, 1i9, then the number of elements in the set A is
EASY
A set T is given as T=xR(x-3)=(x+4)2,x<2. Which of these would be TRUE about the set T ?
MEDIUM

If 

A=x:x is a natural number less than is 6

B=x:x is a pime number which is a divisor of 60

C=x:x is an odd natural number less than 10

D=x:x is an even natural number which is a divisor of 48

Then write roster form for all above sets and find A-D

MEDIUM

If 

A=x:x is a natural number less than is 6

B=x:x is a pime number which is a divisor of 60

C=x:x is an odd natural number less than 10

D=x:x is an even natural number which is a divisor of 48

Then write roster form for all above sets and find BC

MEDIUM
Write A={3, 9, 27, 81} in set builder form.
MEDIUM

If 

A=x:x is a natural number less than is 6

B=x:x is a pime number which is a divisor of 60

C=x:x is an odd natural number less than 10

D=x:x is an even natural number which is a divisor of 48

Then write roster form for all above sets and find D-B

EASY
Out of 80 students who appeared for the school exams in Mathematics M, Physics P and Chemistry C, 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is
EASY
If A=x:x is a factor of 24,then find nA
EASY
In an examination, 54% of the candidates passed in science and 42% failed in mathematics. If 32% failed in both subjects, what percentage passed in both subjects ?
HARD

Let A be the set of vectors a=a1,a2,a3 satisfying i=13ai2i2=i=13ai22i. Then,

HARD
Let A, B and C  be sets such that ϕABC. Then which of the following statements is not true?