MTH405 MidTerm Quiz by taleemi markaz 2024

MTH405 MidTerm Quiz by taleemi markaz 2024 Part 1 For More Lectures Keep visiting our Channel "TALEEMI MARKAZ". Don't Forget to Subscribe our Channel. Thanks #MTH405Quiz1 #mth405midquiz #mth405quizno1 #mth405midterm #MetricSpace Questions: 𝒂∗𝑯=𝑯∗𝒂 relation holds if _______ The operation of addition '+' satisfies the commutative property The set of nth roots of unity is a cyclic group under If a,b are the elements of group G, then (𝒃^(−𝟏) 𝒂^(−𝟏) )^(−𝟏)=____ The set {1,-1} is a group under addition. If X has 4 element, then total number of permutations on X is _______ Subtraction is a binary operation on the set of Real numbers R. The group (Z,+) is a finite group If G is an abelian group and H is subset of G, then 𝒂𝑯=𝑯𝒂 for some a in G. If X consists of the elements 1,2,....7, then the symbol (1,3,4,2,6) means the permutation ______ If 𝒇=(■8(𝟏&𝟐&𝟑@𝟐&𝟏&𝟑)) 𝒂𝒏𝒅 𝒈=(■8(𝟏&𝟐&𝟑@𝟐&𝟑&𝟏)) are two permutations, then their product permutation, 𝒇𝒈=(■8(𝟏&𝟐&𝟑@𝟑&𝟏&𝟐)) Under multiplication, 1 is not an idempotent element A non-empty set with the ____ binary operation is Semigroup. A non-empty set with a binary operation is called _____ The set of real numbers is an abelian group under A cycle of length ____ is called the transposition. Every cyclic permutation can be expressed as a _____ of transpositions. The length of cyclic permutation (■8(𝒂_𝟏&𝒂_𝟐&𝒂_𝟑@𝒂_𝟐&𝒂_𝟑&𝒂_𝟏 )) is The set G={1,-1,i,-i} is a NOT group under multiplication. The group {1,-1} is subgroup of the group {1,-1,i,-i} The set of natural numbers N starts from 1. A group G is abelian if and only if (𝒂𝒃)^𝟐=𝒂^𝟐 𝒃^𝟐 for all 𝒂, 𝒃∈𝑮 The length of the cyclic permutation is (■8(𝟐&𝟑&𝟏&𝟒&𝟓&𝟔@𝟏&𝟑&𝟓&𝟒&𝟐&𝟔)) If X has 4 element, then total number of permutations on X is _______ If index of H in G is 4, then there are 4 _________ If index of H in G is 4, then there are 4 _________ The operation of addition '+' satisfies the commutative property Is the following true or false? (■8(𝟏&𝟐&𝟑@𝟐&𝟑&𝟏))(■8(𝟏&𝟐&𝟑@𝟑&𝟏&𝟐))=(■8(𝟏&𝟐&𝟑@𝟏&𝟐&𝟑)) The group (G,*) is said to be an abelian group or commutative group if for all 𝒂,𝒃∈𝑮, 𝒂∗𝒃= Let order of a group be 35. Which of the following CANNOT be the order of the subgroup of G?