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SIXTH GRADE / BASICS of SET THEORY / TEST 2.1.2

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH.
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

SOME OF OUR QUESTIONS ARE REALLY HARD, FOR THOSE THAT ARE SKILLED IN MATH.
SKIP THEM IN CASE NOT FOR YOU.

IF YOU DESIRE SO, WE CAN DISCUSS HARD/INTERESTING QUESTIONS IN OUR FORUM.

  SET THEORY
 ♦ 
IS THE FIRST ABSTRACT SUBJECT in MATH.  SOME TERMS of IMPORTANCE are ELEMENT, INTERSECTION, UNION, EMPTY SET, UNIVERSAL SET, COMPLEMENT.
 ♦ IDEMPOTENT, COMMUTATIVE, ASSOCIATIVE, DISTRIBUTIVE, IDENTITY, COMPLEMENT, De MORGAN'S LAWS and CONSISTENCY PRINCIPLE are INPORTANT PROPERTIES.

THEY FORM THE FOUNDATION of THE THORY of PROBABILITY which is THE TRUE LOGIC of THE WORLD.

    Ref.-1         Ref.-2
1. n(A) + n(B) - n(C) = ?

!


a) 5
b) 8
c) 3
d) 7
n(A)denotes the number of elements of a set .
2. A ∩ B ∩ C = ?

!


a) A
b) B
c) ∅
d) C
No 2 real bodies are the same .
3. The sets A = {blue balloon, red balloon, green balloon} , B = {blue balloon, red balloon, green balloon, yellow balloon, purple balloon, turquoise balloon} and C = {blue balloon, red balloon, green balloon, yellow balloon, purple balloon} are given. A ∩ B ∩ C = ?

a) A
b) B
c) C
d) {blue balloon, red balloon, green balloon}
We make them the same as we name. It is better though, so we can go further.
4. The sets A = {1, 3, 5, 7, 9}, B = {-3, -1, 0, 5, 7, 9} ve C = {x | x is a whole number (ınteger, positive and negative)} are given. Which element(s) should be within the light blue area with a question mark in ?

!


a) {1, 3, 5, 7, 9}
b) {5, 7, 9}
c) A ∩ B
d) A
Elements both in A and in B are questioned .
5. The sets A = {1, 3, 5, 7, 9}, B = {-3, -1, 0, 5, 7, 9} ve C = {x | x is a natural number} are given. Which element(s) should be within the light blue area ?

!


a) C ∩ {-3, -1, 0}
b) C
c) C ∪ {-3, -1, 0}
d) ∅
0 and negative integers are not in natural numbers .
y
6. Which set is equal to the set A = {1, 9, 25, 49, 81, 121} ?

1- A = {x | x is square of an integer}
2- B = {x | x < 12 & x is an integer}
3- C = {x2 | -12 < x < 12 & x is an integer}
4- D = {x2 | x2 < 121 & x is an odd integer}
5- E = {x2 | -12 < x < 12 & x is an odd integer}


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) only 1
b) 1 and 4
c) only 4
d) 4 and 5


Integers are positive and negative natural numbers (and zero).
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7. Which of the following choices is correct ?

a) {6,4,10} ∈ {2,4,6,8,10}
b) ∅ ∪ {6,4,10} ⊆ {2,4,6,8}
c) {6,4,10} ∩ {2,4,6,8,10} = ∅
d) ∅ ∩ {6,4,10} ⊆ {2,4,6,8,10}
⊆ denote a subset or a proper subset .
8. Which set is identical to the set A = {5, 7, 11, 13, 17} ?

a) B = {x | 3 < x < 18 & x is an odd natural number}
b) B = {x | 5 < x < 18 & x is an odd natural number}
c) B = {x | x < 18 & x is a prime number}
d) B = {x | 1 < x < 18 & x is an odd natural number}
< , means less than .
9. A ∪ B = ?

!


a) {2,3,5,7,11,13,15,17,19}
b) {1,2,3,5,7,11,13,15,17,19}
c) {2,3,5,7,13,15,17,19}
d) A
A = {2,3,5,7,11,13,17} and B = {5} .
10. The sets A = {letters of "ATLANTA"} and B = {letters of "ANTALYA"} are given. A ∪ B = ?

a) A
b) ∅
c) B
d) {A,T,L,N,A}
A = {A,T,L,N} , B = {A,N,T,L,Y} .
11. Which is a 2-element subset of A ?

!


a) {rose, CURRENT}
b) {0, CURRENT}
c) {0, rose}
d) all
"rose" is not an element, the set has a picture not a word .
y
12. How many 4-element subsets should the set given in the picture of the previous question have ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 5
b) 8
c) 4
d) 10
Have please a look at ry1 .
13. Which of the following sets are identical to A = {2} ?

1- {A| A is an even prime}
2- {A| A is an integer and A2=4}
3- {A| A the smallest even natural number}


a) only 4
b) 2 and 4
c) only 1
d) 1 and 3
(-2)2 = -2 x -2 = 4 .
14. Which choice is correct according to the Venn diagram below ?

!


a) none
b) {4} = (A ∩ B) \ (C ∩ B)
c) {4} = (A ∩ B) ∪ (C ∩ B)
d) {4} = (A ∩ B) ∩ (C ∩ B)


(A ∩ B) \ (C ∩ B) and (A ∩ B) - (C ∩ B) are the same.
15. Which is wrong for A = {SOUTH , CAROLINA} ?

a) ∅ = A
b) SOUTH ∈ A
c) {CAROLINA} ⊂ A
d) s(A) = 2
Elements are separated by commas .
16. The sets A \ B = {x | 1 ≤ x ≤ 7 and x is odd natural number } , B = {x | 2 ≤ x ≤14 ve x and x is even natural number} and A ∪B = {x | x ≤ 14 and x is natural number} are given. Which choice(s) is/are correct ?

!


a) all
b) none
c) 2
d) 1
9, 11, ...
17. How many elements should be added to B of the previous question to attain a correct picture ?

a) 1
b) 2
c) 3
d) 4
9,11 ... .
y
18. The 7-element sets A,B and C are given with incomplete Venn diagrams. The numbers or letters in different regions show the number of elements that are in this region and different letters correspond to different numbers. What should M be ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2


a) 2
b) 1
c) 3
d) 0
It should be K ∈ {0,1,2} , M ∈ {0,1,2} and N ∈ {0,1,2}, because they should be unequal with a sum of 3 . Have please a look at ry1 for further help.
19. Which of the following sets has the same cardinality with A ={ x | x=a/b , a and b natural numbers} ?

a) none
b) {x | x is a natural number}
c) {a,b}
d) ∅
Corresponding to every pair of a and b we can find a natural number .
20. Which is identical to the difference set (A ∪ B) \ C ?

!


a) A
b) C
c) ∅
d) A ∪ B
C covers all .
21. Take the figure given in the previous question and let B = {1,2,3}, C = {all numbers in Pascal triangle}. Which choice will be correct ?

a) {1,2,3}
b) {1,2,3,4,5}
c) ∅
d) B ∪ C = {x| x is natural number}
Each natural number is in Pascal triangle .
y
22. The 7-element sets A,B and C are given with incomplete Venn diagrams. The numbers or letters in different regions show the number of elements that are in this region without any other constraint. What should M be ?

!


In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) 1
b) 1 and 5
c) 3
d) 1 and 2


Like question-18 but this time K,L,M and N may be the same numbers. Have a look at ry1 .
23. In a class of 60 students numbered 1 to 60, all even numbered students come to school by bus, the ones whose numbers are divisible by 3 come by taxi and those whose numbers are divisible by 5 come by family car. Rest come by walking. How many students do then come by walking ?

a) 15
b) 13
c) 16
d) 17
The number 1, those with prime numbers, ... ?
24. Though the number of students of the class in the previous question is 60 and though there are 30 students whose numbers are divisible by 2, 20 by 3 and 12 by 5 which has a total of 62, some students come by walking. Why ?

a) s({number divisible by 2} ∩ {number divisible by 3}) = 10
b) s({number divisible by 2} ∩ {number divisible by 5}) = 6
c) s({number divisible by 3} ∩ {number divisible by 5}) = 4
d) tümü
Among numbers from 1 to 60 there are numbers dibisible both by 2 and by 3 .
25. Which students come by walking though their numbers are not prime ?

!


a) only 1
b) 1 and 49
c) only 49
d) 1, 18 and 49
1 is not prime .
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2012 , İsmail GERMAN. ALL RIGHTS RESERVED
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