The binary operation * defined on N by a * b = a + b + ab for all… - Vidyadip

MCQ

The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is:

A
Commutative only.
B
Associative only.
✓
Commutative and associative both.
D
None of these.

✓

Answer

Correct option: C.

Commutative and associative both.

a * b = a + b + ab
b * a = b + a + ba
⇒ a * b = b * a
So * is commutative.
Now,
(a * b) * c
= (a + b + ab) * c
= a + b + ab + c + ca + cb + abc
a * (b * c)
= a * (b + c + bc)
= a + b + c + bc + ab + ac + abc
⇒ (a * b) * c = a * (b * c)
So * is associative.

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