Let * be a binary operation on N defined by a * b = a + b + 10 fo… - Vidyadip

Question

Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is:

−10
0
10
Non-existent.

✓

Answer

Non-existent.

Solution:

Given a * b = a + b + 10

Let the identity element be e, then

a * e = a

⇒ a + e + 10 = a

⇒ e = -10

But the operation is defined on the set of natural numbers.

So, the identity element doesn't exist.

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