Practice Definition Of Groups (13.1) - Group Theory - Discrete Mathematics

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6 sample questions

Question 1.
What is the definition of a group?
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Remember the four key properties.
Question 2.
Can a set of non-negative integers form a group under addition?
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Consider what happens when you try to find the inverse of an element.
3Question 3.
What defines a group in mathematics?
- A set with addition
- A set with a binary operation satisfying certain axioms
- Any collection of numbers
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Think about the requirements needed for a group.
4Question 4.
Is the identity element unique in a group?
- True
- False
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Consider the definition of identity in groups.
Question 5.
Consider the set of rational numbers under addition. Does it form a group? Justify your answer using the group axioms.
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Check each axiom systematically.
Question 6.
Propose a new operation on a set of your choice and prove whether or not it forms a group.
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Define your operation clearly and work through examples.

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