Mark the correct alternative in the following question for the bi… - Vidyadip

MCQ

Mark the correct alternative in the following question for the binary operation $*$ on $Z$ defined by $a^ * b = a + b + 1,$ the identity element is:

A
$0$
✓
$-1$
C
$1$
D
$2$

✓

Answer

Correct option: B.

$-1$

We have,
$a^ * b = a + b + 1$
Let e be the identity element of $*.$ Then,
$a^ * e = a = e^ * a$
$a + e + 1 = a$
$e = a - a - 1$
$e = -1$

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