Discrete Maths - Sets
38. Which of the following statements is FALSE ?
- Option : D
- Explanation : Set of rational numbers form an abelian group under multiplication . It satisfies with 0 also. As we know abelian group follow some properties:1. associative i.e. ao(boc)= (aob)oc for 0 0*(1*2)=0 and (0*1)*2=0 so this property has prove2. If an element 4 belongs to G such that 0o4=0 for all 0 belongs to G3. For any a belongs to G and b belongs to G such that aob=e for ex: a=0 b=2 For * 0*2=0 and 0 is identity(e) for multiplication4. For commutative property 0*4=4*0=0So all properties of abelian group are followed by 0 also so statement is correctSo answer is (D)
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