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Question: Answered & Verified by Expert
If $Q_{1}$ is the set of all relations other than $1$ with the binary operation * defined by $a * b=a+b-a b$ for all $a, b$ in $Q_{1}$, then the identity in $Q_{1}$ with respect to $*$ is
MathematicsMathematical ReasoningCOMEDKCOMEDK 2013
Options:
  • A $1$
  • B $0$
  • C $-1$
  • D $2$
Solution:
1771 Upvotes Verified Answer
The correct answer is: $0$
Let $e$ be the identity element, then
$a$ * $\boldsymbol{e}=a$
$\Rightarrow \quad a+e-a e=a$
$\Rightarrow \quad e(1-a)=0$
$\Rightarrow \quad e=0 \quad[a \neq 1]$

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