On This Page
This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 10
Q1 | a * H is a set of coset.
- right
- left
- sub
- semi
Q2 | a * H = H * a relation holds if
- h is semigroup of an abelian group
- h is monoid of a group
- h is a cyclic group
- h is subgroup of an abelian group
Q3 | Lagrange’s theorem specifies
- the order of semigroup is finite
- the order of the subgroup divides the order of the finite group
- the order of an abelian group is infinite
- the order of the semigroup is added to the order of the group
Q4 | A function is defined by f(x)=2x and f(x +y) = f(x) + f(y) is called
- isomorphic
- homomorphic
- cyclic group
- heteromorphic
Q5 | An isomorphism of a group onto itself is called
- homomorphism
- heteromorphism
- epimorphism
- automorphism
Q6 | The elements of a vector space form a/an under vector addition.
- abelian group
- commutative group
- associative group
- semigroup
Q7 | A set of representatives of all the cosets is called
- transitive
- reversal
- equivalent
- transversal
Q8 | Which of the following statement is true?
- the set of all rational negative numbers forms a group under multiplication
- the set of all matrices forms a group under multiplication
- the set of all non-singular matrices forms a group under multiplication
- the set of matrices forms a subgroup under multiplication
Q9 | How many different non-isomorphic Abelian groups of order 8 are there?
- 5
- 4
- 2
- 3
Q10 | Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings
- does not form a group
- does not have the right identity element
- forms a non-commutative group
- forms a group if the empty string is removed from
Q11 | All groups satisfy properties
- g-i to g-v
- g-i to g-iv
- g-i to r-v
- r-i to r-v
Q12 | An Abelian Group satisfies the properties
- g-i to g-v
- g-i to r-iv
- g-i to r-v
- r-i to r-v
Q13 | A Ring satisfies the properties
- r-i to r-v
- g-i to g-iv
- g-i to r-v
- g-i to r-iii
Q14 | A Ring is said to be commutative if it also satisfies the property
- r-vi
- r-v
- r-vii
- r-iv
Q15 | An ‘Integral Domain’ satisfies the properties
- g-i to g-iii
- g-i to r-v
- g-i to r-vi
- g-i to r-iii
Q16 | a.(b.c) = (a.b).c is the representation for which property?
- g-ii
- g-iii
- r-ii
- r-iii
Q17 | a(b+c) = ac+bc is the representation for which property?
- g-ii
- g-iii
- r-ii
- r-iii
Q18 | For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn?
- n
- n-1
- 2n
- n!
Q19 | Does the set of residue classes (mod 3) form a group with respect to modular addition?
- yes
- no
- can’t say
- insufficient data
Q20 | Does the set of residue classes (mod 3) form a group with respect to modular addition?
- yes
- no
- can’t say
- insufficient data
Q21 | The less-than relation, <, on a set of real numbers is
- not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
- a partial ordering since it is asymmetric and reflexive
- a partial ordering since it is antisymmetric and reflexive
- not a partial ordering because it is not antisymmetric and reflexive
Q22 | If the longest chain in a partial order is of length l, then the partial order can be written as disjoint antichains.
- l2
- l+1
- l
- ll
Q23 | Suppose X = {a, b, c, d} and π1 is the partition of X, π1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by
- 15
- 10
- 34
- 5
Q24 | The inclusion of sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment.
- {1}, {2, 4}
- {1}, {1, 2, 3}
- {1}
- {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
Q25 | Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true?
- every non-empty subset of has a greatest lower bound
- it is uncountable
- every non-empty finite subset of has a least upper bound
- every non-empty subset of has a least upper bound