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SIXTH GRADE / BASICS of SET THEORY / TEST 2.1.3

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. Which choice is the light blue region ?

!


a) (B ∩ C) ∪ (A ∩ B ∩ C
b) (B ∩ C) ∩ (A ∩ B ∩ C
c) (B ∩ C) \ (A &u; B ∪ C
d) (B ∩ C) \ (A ∩ B ∩ C)
The intersection of the 3 sets is in the middle .
2. Any sets A = {} , B ={} ve C = {} are given. (A ∪ B ∪ C) ∩ (A ∩ B ∩ C) = ?

!


a) green region
b) grey region
c) purple region
d) blue region
(A ∪ B ∪ C) is relatively universal, the intersections are basic in this case .
3. What will be the minimal number of elements of (A ∪ B ∪ C) for any A, B, C ?

a) 1
b) 0
c) 3
d) 2
All sets may be ∅ .
4. The sets A = {1, 3, 5, 7, 9}, B = {-3, -1, 0, 5, 7, 9} and C = {x | -21 < x < 21, x is an integer} are given. Which choice below gives the odd integers in the light blue region with a question mark in ?

!


a) {-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 11, 13, 15, 17, 19}
b) {-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 11, 13, 15, 17, 19}
c) {-19, -17, -15, -13, -11, -9, -7, -5, 11, 13, 15, 17, 19}
d) {-17, -15, -13, -11, -9, -7, -5, 11, 13, 15, 17}
The elements that are in C but not in A and not in B .
5. Which prime numbers are in the right answer to the previous question ?

a) {-19, -17, -13, -11, -7, 11, 13, 15, 17, 19}
b) {11, 13, 17, 19}
c) {7, 11, 13, 17, 19}
d) {11, 13, 15, 17, 19}
Primes are a proper subset of naturals .
y
6. Let the subset of positive integers of the right answer to question 4 be P and the negative integers subset be N. What will be the number of subsets of N with number of elements less than or equal to S(P)/S(N) ?

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



a) 37
b) 43
c) 34
d) 49


S(P)/S(N) = 2. The number of subsets that have 0,1 and 2 elements is being questioned .
ClickN KIDS Beginning Reading & Spelling Programs Teacher Created Resources ClickN KIDS Beginning Reading & Spelling Programs
7. A given set has 28 of 2-element subsets. Its intersection with a 6-element set B, in addition, has 5 elements. What will be the number of elements of A\B ?

a) 4
b) 6
c) 3
d) 5
A should have 8 elements 5 of which is common with B .
8. The set A = {5, 7, 11, 13, 17} is given with its (relative) universal set E having 17 elements. How many elements should E\A have ?

a) 16
b) 11
c) 14
d) 12
If the focus is on a family with a father, a mother, a mother-in-law and 3 children, the universal set has 6 members .
9. For which set is the equality A=∅ true ?

a) A={D | Dx0 ∈ natural numbers}
b) A={∅}
c) A={D | D/0 ∈ natural numbers}
d) A={x | x is an even prime}
Infinity is a concept, not a number; otherwise 1/0 = 2/0 could not be. Even 0/0 is not a unique number .
10. A 3-element subset of the digits 0 to 9 is given. How many elements will have the set of possible cases of the sets of 3-digit numbers constructable with these digits using each only once ?

a) 2
b) 3
c) 5
d) 1
Depending on 0 is among the given digits or not ... .
11. The numbers indicate the number of elements in respective regions and s(A∪B) = 30. What is the number of elements of B ?

!


a) 18
b) 22
c) 15
d) 12
The total number of elements, seen or unseen, is 40, i.e. 8 elements are not seen .
y
12. In a class of 27 students 17 play a sport as an amateur and 12 applied to model/actress agencies. What will be the minimum and maximum number of students that do both ?

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

RY1 RY2



a) 2 and 10
b) 3 and 12
c) 4 and 10
d) 2 and 12
If all students were to participate in any, it would be 2 students ... Have please a look at ry1 .
13. Which of the following sets are identical to the set given in the figure below ?

!


a) {x | x integer, x<13}
b) {x | x prime, x <13} ∪ {1,4,6,8,9,10,12}
c) {x | x integer, x<12}
d) {x | x prime, x <13} ∪ {1,4,6,8,9,10}
If we claim 1, we need to consider -7 ...
14. How many elements does the set of squares in the figure below have ?

!


a) 36
b) 28
c) 30
d) 40


1 with side 4, 4 with side 3, 9 with side 2 and 16 with side 1 + ...
15. The number of children playing is not known but the sum of their ages is known to be 8. Which set gives the case of maximal product (of ages) ?

!


a) {2,2,2,2}
b) {3,3,2}
c) {3,3,3}
d) {2,4,2}
Ages should be as close as possible to each other but the number of children is not known ...
16. The sets and properties A={1,2,3,4}, A∩B={2,3,4} and A∪B={2,3,4,5,7} are given. B = ?

a) B={1,3,7}
b) B={1,5,7}
c) B={1,2,7}
d) B={1,2,5,7}
The elements of intersection are to be in both (all) intersecting .
17. s(A) + s(B) = ?

!


a) 56
b) 62
c) 48
d) 54
The elements of intersection are to be in both (all) intersecting .
y
18. How many subsets of {T,E,S,T,D,O,C,T,O,R} are to be constructed with the consonants only ?

!


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


a) 35
b) 27
c) 31
d) 44
The set is of course {T,E,S,D,O,C,R} olup and it has 7 elements. For further help have please a look at ry1 .
19. Which choice gives B if A ∪ B = {a,b,c,d,e} and B ∪ C = {c,d,e,f,g,h} ?

a) noe
b) {c,d,e}
c) C
d) ∅
B = {elements of both sets} .
20. What is the intersection of a sphere and a plane ?

a) ellipse
b) line segment
c) circle
d) conic
A sphere has spherical symmetry .
21. What is the intersection set of a plane (table) and the shadow (cylinder) of a sphere ?

!


a) line segment
b) circle
c) line
d) ellipse
Rays are a parallel beam .
y
22. How many of the subsets of the set A = {a,b,c,d,e,f,g} contain all 3 of a, b and c ?

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

RY1 RY2



a) 24
b) 16
c) 32
d) 8


These letters alone construct 23=8 subsets. The others on the other hand construct 24=16 subsets. Altogether 27= 8 x 16 = 128 subsets can be constructed. For further help have please a look at ry1.
23. The sets B = {a,b,c,d,e} ve C = {c,d,e,f,g,h} are given. s(C&cupB)/s(C\B)=?

a) 16
b) 32
c) 28
d) 42
C&cupB={a,b,c,d,e,f,g,h} and C\B = {f,g,h}
24. The sets A = {3,6,12,24,48}, B = {4,8,12,16, ...,60} and C = {6,12,18,...,60} are given. A ∩ B ∩ C = ?

a) {12,24,48}
b) {12,24}
c) {6,12,24,48}
d) {3,6,12,24,48}
"..." means the pattern is to be kept to fill in .
25. The sets A = {3,6,12,24,48}, B = {4,8,12,16, ...,60} and C = {6,12,18,...,60} are given. (A \ B) \ C = ?

a) 3
b) 3,6
c) {3}
d) {3,6}
(A \ B) = {3,6} .
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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