Problem 1
Let ∗ be a binary operation on set of rational number Q defined as follows: a∗b=a+b+2ab, where a, b ∈ Q,
a) Prove that ∗ is commutative, associative algebraic operation on Q.
b) Find the identity element if any. Solution.
c) Find the zero element if any .
d) Find all invertible elements if any

Problem 2.
a) Verify that the relation defined on set of integers Z by R7 ={(m,n) | 7 divides (m³ −n³)}⊂Z×Z is equivalence relation CLARIFICATION NOTE: (m³ same as m to the POWER OF 3)
b) Describe equivalence classes of relation R7.

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