Which of the following is TRUE ?
| A. | Set of all rational negative numbers forms a group under multiplication |
| B. | Set of all non-singular matrices forms a group under multiplication |
| C. | Set of all matrices forms a group under multipication |
| D. | Both (b) and (c) |
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Option: B Explanation : Click on Discuss to view users comments. |
The set of all nth roots of unity under multiplication of complex numbers form a/an
| A. | semi group with identity |
| B. | commutative semigroups with identity |
| C. | group |
| D. | abelian group |
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Option: D Explanation : Click on Discuss to view users comments. |
Which of the following statements is FALSE ?
| A. | The set of rational numbers is an abelian group under addition |
| B. | The set of rational integers is an abelian group under addition |
| C. | The set of rational numbers form an abelian group under multiplication |
| D. | None of these |
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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)
Click on Discuss to view users comments. waqas said: (10:35pm on Thursday 26th September 2013)
in option C the statement shoud be The set of non zero rational numbers forms an abelian group under multiplication
Vinodh Routhu said: (7:14pm on Sunday 24th August 2014)
the set of rational numbers satisfy abelian group under addition and multiplication
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In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is
| A. | 6 |
| B. | 8 |
| C. | 4 |
| D. | 2 |
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Option: A Explanation : Click on Discuss to view users comments. |
