Question 7.Prove or disprove:(a) The union of two subgroups of a group (G, *) is a subgroup of G.(a) The intersection of two subgroups of a group (G, *) is a subgroup of G.Question 8.Define a relation~ on the set of rational numbers Q bya v b iff a| = |b|(a) Prove that ~ is an equivalence relation on Q. State clearly the properties ofthat are used in the proof.= on(b) Give a complete set of equivalence class representatives for v.

7) We need to prove or disprove the given statements. a) The union of two subgroups of a group G ,…

Answered: Question 7. Prove or disprove: (a) The…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 44E: 44. Let be a subgroup of a group .For, define the relation by ...

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44. Let be a subgroup of a group .For, define the relation by if and only if . Prove that is an equivalence relation on . Let . Find , the equivalence class containing .
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