Let Z be the group of all integers under the operation of addition. E.pdf

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Let Z be the group of all integers under the operation of addition. Explain why the subset {n belongs to Z: n greaterthanorequalto 0} is not a subgroup of Z. Solution Identity element of given group is 0.. and the inverse of an element \'a\' is \'-a\'.. means the negative counterparts of postive numbers..which are missing in the group.. since we have only number which are greater than or equal to 0.. hence inverses are missing..therefore it is not a group itself...

Let Z be the group of all integers under the operation of addition. Explain why the subset {n
belongs to Z: n greaterthanorequalto 0} is not a subgroup of Z.
Solution
Identity element of given group is 0..
and the inverse of an element 'a' is '-a'..
means the negative counterparts of postive numbers..which are missing in the group..
since we have only number which are greater than or equal to 0..
hence inverses are missing..therefore it is not a group itself..

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