Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2009
Easy
Which one of the following is NOT necessarily a property of a Group?
- Commutativity
- BAssociativity
- CExistence of inverse for every element
- DExistence of identity
Explanation
The group axioms require closure, associativity, an identity element, and inverses for every element — but NOT commutativity (a group satisfying commutativity is specifically called an abelian group, a stronger, separate condition).
Source: GATE CS 2009 (2009)
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