Set, Relation, Group, and Function MCQs
Engineering Mathematics:-Set, Relation, Group, and Function MCQs || Cartesian product, the law of algebra related to set, lattice MCQs || Related MCQs for different Engineering Examination such as University Exams, PSU Exams, and all other govt. job Examinations.
Q1.A well defined collection of objects is called a
[ VVIQ]
(A).Set
(B).Relation
(C).Function
(D).Group
Q2.Null set is the subset of
[ VVIQ]
(A).Every set
(B).Super set
(C).Power set
(D).All of the above
Q3.If AÍ ≠
[ VVIQ]
(A). proper subset
(B).subset
(C).power set
(D).super set
Q4.Which of the following is an empty set?
[ VVIQ]
(A).ɸ
(B).{ }
(C).{ɸ}
(D).A and B
Q5.The total no of elements in a set is called
[ VVIQ]
(A).cardinality
(B).domain
(C).range
(D).None of these
Q6.Find the power set of a given set:
A={1,2,3}
[ VVIQ]
(A).8
(B).6
(C).1
(D).0
Q7.If A and B are nonempty sets, then the cardinality of A and B are 2 & 3 respectively then cardinality A×B is
[ VVIQ]
(A).6
(B).5
(C).13
(D).4
Q8.The number of all possible proper subsets of any set A is:
[ VVIQ]
(A).2^n
(B).2^n-1
(C).2^n-2
(D).2n-1
Q9.A∆B=
[ VVIQ]
(A).(A-B)ᴜ(B-A)
(B).(A-B)∩ (B-A)
(C).(B-A).(A-B)
(D).None of these
Q10.If A contains n elements then the number of elements in power set of A is:
[ VVIQ]
(A).n^2
(B).n!
(C).2n
(D).2^n
Q11.The number of all possible subsets of {2,{5,6}} is:
[ VVIQ]
(A).2
(B).4
(C).6
(D).8
Q12.In a survey, it was found that 63%. Indian like apples and 76% like oranges. How many Indians like both?
[ VVIQ]
(A).13%
(B).6.5%
(C).39%
(D).19.5%
Q13.If A and B are subsets of a set X such that x(X)=900, n(A)=300, n(B)=400 and n(A∩B)=150, Then n(A'∩b')=?
[ VVIQ]
(A).250
(B).400
(C).450
(D).350
Q14.A Relation R is called an equivalence relation if
[ VVIQ]
(A).R is reflexive and transitive
(B).R is reflexive and symmetric
(C).R is reflexive, transitive and symmetric
(D).R is reflexive, transitive and anti-symmetric
Q15.Let S be the set of all real numbers. Then the relation R={(a,b):1+ab>0} on S is:
[ VVIQ]
(A).Reflexive and symmetric but not transitive
(B).Reflexive and transitive but not symmetric
(C).Symmetric and transitive but not symmetric
(D).None of these
Q16.Which of the following relation is a reflexive relation of the given set A={1,2,3}?
[ VVIQ]
(A).R1={(1,1),(2,2),(3,3)}
(B).R2={(1,1),(2,2)}
(C).R3={(1,1),(2,2),(3,3),(1,2)}
(D).Both option A & C
Q17.Which of the following relation is a symmetric relation of the given set A={1,2,3,4}?
[ VVIQ]
(A).R1={(1,2),(1,3),(2,1),(2,2),(3,1)}
(B).R2={(1,2),(2,2),(1,1),(3,3),(4,4)}
(C).R3={ }
(D).Both option R1 & R3
Q18.Which of the following relation is a transitive relation of the given set
A={1,2,3} ?
[ VVIQ]
(A).R1={ }
(B).R2={(1,1),(1,2),(2,1)}
(C).R3={(1,2),(2,1),(2,3)}
(D).Both option A & B
Q19.The function , f:R->R: f(x)=cosx is:
[ VVIQ]
(A).one-one, onto
(B).one-one, into
(C).many-one, onto
(D).many-one, into
Q20.The function f:R->R:f(x)=x3 is:
[ VVIQ]
(A).many-one, into
(B).one-one, onto
(C).many-one, onto
(D).None of these
Q21.The function f:C->R:f(z)=|Z| is :
[ VVIQ]
(A).many-one, into
(B).many-one, onto
(C).one-one, into
(D).None of these
Q22.If A={1,2,3}, B={4,5}, C={1,2,3,4,5}, then (C× B)-(A ×B)=
[ VVIQ]
(A).(C-A)×(B-A)
(B).B×B
(C).(C∩A)×B
(D).None of these
Q23.Which one is a singleton?
[ VVIQ]
(A).{0,1}
(B).{1,11,111}
(C).{0}
(D).{1,2}
Q24.The mapping f:N->N defined by f(n)=[n+1/2], n∈N is
[ VVIQ]
(A).injective
(B).surjective
(C).bijective
(D).None of these
Q25.The inverse of function f(x)=x3 +2 is...........
[ VVIQ]
(A).f^-1(y)=(y-2)^1/2
(B).f^-1(y)=(y-2)^1/3
(C).f^-1(y)=(y)^1/3
(D).f^-1(y)=(y-2)
Q26.The power set of an empty set has exactly...............subset.
[ VVIQ]
(A).one
(B).two
(C).zero
(D).three
Q27.Let R be a relation on N, defined by:
R={(x,y):x,y∈ N and 2x+y=4}
Then, R is:
[ VVIQ]
(A).Reflexive
(B).Symmetric
(C).Transitive
(D).None of these
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