1 votes 1 votes $\text{Prove that : the union of any two subgroup of 'G' is not subgroup of 'G'}$ $\text{Prove that : the intersection of any two subgroup of 'G' is also a subgroup of 'G'}$ Set Theory & Algebra discrete-mathematics set-theory&algebra group-theory zeal zeal-workbook + – Prince Sindhiya asked Aug 22, 2018 edited Mar 9, 2019 by ajaysoni1924 Prince Sindhiya 320 views answer comment Share Follow See 1 comment See all 1 1 comment reply Kabir5454 commented Sep 11, 2022 reply Follow Share Counter example for Statement 1:- $G_{1}=\left ( 2\mathbb{Z},+ \right )$ $G_{2}=\left ( 3\mathbb{Z},+ \right )$ $G_{1}\cup G_{2}=\left ( 2\mathbb{Z}\cup 3\mathbb{Z},+ \right )$ Now as ,$G_{1}\cup G_{2}$ is a group so it must be closed but it isn’t as , $5$ should be in $G_{1}\cup G_{2}$ but it isn’t . 0 votes 0 votes Please log in or register to add a comment.