Set theory Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). \( \Large A- \left(B \cap C\right) \) is equal to
A). \( \Large \left(A-B\right)\cap \left(A-C\right) \)
B). \( \Large \left(A-B\right)\cup \left(A-C\right) \)
C). \( \Large \left(A\cap B\right)-C \)
D). None of these
2). If A = \( \Large \{ x : x^{2} = 1 \} \) and B \( \Large \{ x : x^{4} = 1 \} \), then \( \Large A \cup B \) is equal to:
A). {i, -i}
B). {-1, 1}
C). {-1, 1, i. -i}
D). None of these
3). If A = \( \Large \{ x : x = 4n+1, 2 \le n \le 5 \} \) then number of subsets of A is:
A). 16
B). 15
C). 4
D). none of these
4). Let R and S be two relations on a set A. Then which is not correct?
A). R and S are transitive, then R u S is also transitive.
B). R and S are transitive, then R n S is also transitive.
C). R and S are reflexive, then R n S is also reflexive.
D). R and S are symmetric, then R U S is also symmetric
5). The group of beautiful girls is:
A). a null set
B). a finite set
C). a singleton set
D). not a set


6). R is a relation over the set of real numbers and it is given by \( \Large nm \ge 0 \). Then R is:
A). symmetric and transitive
B). reflexive and symmetric
C). a partial order relation
D). an equivalence relation
7). In a city of 55 students, the number of students studying different subjects are 23 in mathematics, 24 in physics, 19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry, 7 in physics and chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is:
A). 6
B). 9
C). 7
D). all of these
8). If \( \Large N_{a}=\{ an : n \epsilon N \} \), then \( \Large N_{3} \cap N_{4} \) is equal to:
A). \( \Large N_{7} \)
B). \( \Large N_{12} \)
C). \( \Large N_{3} \)
D). \( \Large N_{4} \)
9). The relation "Congruence modulo m" is:
A). reflexive only
B). transitive only
C). symmetric only
D). an equivalence relation
10). Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is:
A). 144
B). 12
C). 24
D). 30
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