Theory Of Computation MCQ

1:

 Which of the following statements are true?
I.    The set of all odd integers is a monoid under multiplication.
II.   The set of all complex number is a group under multiplication
III.  The set of all integers under the operation * given by a * b = a+b-ab is a monoid
IV.   Zs under symmetric difference   defined by
                     A B = (A-B) ∪ (B-A) is an abelian group

A.

I and II

B.

I, III and IV

C.

I, II and III

D.

I, II and IV

 

Answer : B

Explanation :

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Option: A

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