Which of the following statements is FALSE?
1996
Which of the following statements is FALSE?
- A.
The set of rational numbers is an abelian group under addition
- B.
The set of integers is an abelian group under addition
- C.
The set of rational numbers form an abelian group under multiplication
- D.
The set of real numbers excluding zero is an abelian group under multiplication
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Correct answer: C
The set of rational numbers form an abelian group under multiplication
Solution:
A group under multiplication must contain an identity element and every element must have an inverse within the set.
For rational numbers under multiplication, the element 0 has no multiplicative inverse because:
1/0
is undefined.
Hence, the set of all rational numbers is not a group under multiplication.
Therefore, statement (C) is false.
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