The set of all real numbers under the usual multiplication operation is not a group because?
Correct answer: A. zero has no inverse.
- A. zero has no inverse.
- B. Identity element does not exist.
- C. Multiplication is not associative.
- D. Both A and B.
Explanation
Set of real number i.e. (−∞,0)∪(0,∞) is under usual multiplication operation because 0∈R and zero do not have an inverse i.e. it can not give ordered airs to be included in a group.
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Logical deductions require conclusions to be drawn from stated facts, conditions and relationships without adding outside information. The work includes handling all, some and none statements, necessary and sufficient conditions, ordering restrictions, true or false conclusions, and the difference between what must be true and what could be true.
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