Question

$A:AB=A,$ and $BA=B\Rightarrow A^n+B^n=A+B$
$R:AB=A$ and $BA=B\Rightarrow$ A and B are idempotent
The correct answer is

• A. Both A and R are true and R is correct explanation to A
• B. Both A and R are true but R is not correct explanation to A
• C. A is true R is false
• D. A is false R is true

Answer 1

The correct option is A Both A and R are true and R is correct explanation to A

Reason
$A^2=A.A=AB.A$
$=A.BA$
$=A.B$
$=A$
similarly $B^2=B$
hence idempotent and reason is correct explanation of A. $A^n=A.A.A.A......=A$

means $A^n+B^n=A+B$