Question

consider the set Q of rational numbers, and let * be the operation on Q defined by a*b = a+b -ab, then (Q,* ) is:
(1) group (2) semi group (3) commutative group (4) none of the above

Answer 1

Answer:

Step-by-step explanation:

2

Answer 2

Consider the set Q of rational numbers, and let * be the operation on Q defined by a*b = a+b -ab, then (Q,* ) is commutative group. (Option 2)

• A commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative.
• If the commutative law holds in a group, then such a group is called an Abelian group . Thus the group (G,∗) is said to be an Abelian group or commutative group if a∗b=b∗a,∀a,b∈G.

• It is a fundamental property of many binary operations, and many mathematical proofs depend on it.
• In the given binary operation a*b = a+b -ab, then b*a = b+a - ba. Therefore, even after changing the position the result remains the same.

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