On This Page
This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on Discrete Mathematics Set 9
Q1 | If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be?
- 8
- 14
- 22
- 15
Q2 | Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is agroup. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups?
- 65
- 5
- 32
- 18
Q3 | A relation (34 × 78) × 57 = 57 × (78 × 34)can have property.
- distributive
- associative
- commutative
- closure
Q4 | B1: ({0, 1, 2….(n-1)}, xm) where xn standsfor “multiplication-modulo-n” and B2: ({0, 1, 2….n}, xn) where xn stands for “multiplication-modulo-m” are the two statements. Both B1 and B2 are considered to be
- groups
- semigroups
- subgroups
- associative subgroup
Q5 | If group G has 65 elements and it has two subgroups namely K and L with order 14 and30. What can be order of K intersection L?
- 10
- 42
- 5
- 35
Q6 | Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of
- abelian group
- semigroup
- multiplicative group
- isomorphic group
Q7 | Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group?
- closure property
- identity property
- symmetric property
- associative property
Q8 | A group G, ({0}, +) under addition operation satisfies which of the following properties?
- identity, multiplicity and inverse
- closure, associativity, inverse and identity
- multiplicity, associativity and closure
- inverse and closure
Q9 | If (M, *) is a cyclic group of order 73, then number of generator of G is equal to
- 89
- 23
- 72
- 17
Q10 | The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy?
- closure property
- associative property
- symmetric property
- identity property
Q11 | A non empty set A is termed as an algebraic structure
- with respect to binary operation *
- with respect to ternary operation ?
- with respect to binary operation +
- with respect to unary operation –
Q12 | An algebraic structure is called a semigroup.
- (p, *)
- (q, +, *)
- (p, +)
- (+, *)
Q13 | Condition for monoid is
- (a+e)=a
- (a*e)=(a+e)
- a=(a*(a+e)
- (a*e)=(e*a)=a
Q14 | A monoid is called a group if
- (a*a)=a=(a+c)
- (a*c)=(a+c)
- (a+c)=a
- (a*c)=(c*a)=e
Q15 | Matrix multiplication is a/an property.
- commutative
- associative
- additive
- disjunctive
Q16 | How many properties can be held by a group?
- 2
- 3
- 5
- 4
Q17 | A cyclic group is always
- abelian group
- monoid
- semigroup
- subgroup
Q18 | {1, i, -i, -1} is
- a commutative subgroup
- a lattice
- a trivial group
- a monoid
Q19 | Let K be a group with 8 elements. Let H be a subgroup of K and H
- semigroup
- subgroup
- cyclic group
- abelian group
Q20 | is not necessarily a property of a Group.
- commutativity
- existence of inverse for every element
- existence of identity
- associativity
Q21 | A group of rational numbers is an example of
- a subgroup of a group of integers
- a subgroup of a group of real numbers
- a subgroup of a group of irrational numbers
- a subgroup of a group of complex numbers
Q22 | Intersection of subgroups is a
- group
- subgroup
- semigroup
- cyclic group
Q23 | What is a circle group?
- a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements
- a subgroup rational numbers having magnitude 2 of the group of real elements
- a subgroup irrational numbers having magnitude 2 of the group of nonzero complex elements
- a subgroup complex numbers having magnitude 1 of the group of whole numbers
Q24 | A normal subgroup is
- a subgroup under multiplication by the elements of the group
- an invariant under closure by the elements of that group
- a monoid with same number of elements of the original group
- an invariant equipped with conjugation by the elements of original group
Q25 | Two groups are isomorphic if and only if is existed between them.
- homomorphism
- endomorphism
- isomorphism
- association