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EMSTAS Q.38

0. 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 prove 
    2. If an element 4 belongs to  G  such that 0o4=0 for all 0 belongs to G 
    3. 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 multiplication
    4. For commutative property 0*4=4*0=0
    So all properties of abelian group are followed by  0 also  so  statement is correct
    So answer is (D)
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