According to Boolean algebra theorems $x.x$ is equal to
A. $x$
B. 1
C. 0
D. $x'$

Hint: Here in this question we need to perform ‘and’ Boolean operation on $x$ and $x$. We know that “ and” Boolean operation results 1 if both the variables are 1, otherwise 0.

Complete step-by-step answer:
Here from the basic concept of Boolean algebra theorems, for the “and” operation ($.$) between any two Boolean variables $A,B$, the result will be 1 if the value of both $A,B$ are 1 otherwise it will be 0.
From the basic concept of Boolean algebra theorems, for the “or” operation (+) between any two Boolean variables$A,B$, the result will be 1 if any one of the values of both$A,B$is 1 otherwise it will be 0.
From the basic concept of Boolean algebra theorems, for the “not” operation (+) on any Boolean variable$A$, the result will be 1 if its value is 0, otherwise it will be 0.

Here in this question we have to find the value of $x.x$.
$x.x$ will be 1 if $x$ is 1, otherwise it will be 0.
So, we observe that the value of $x.x$ depends on only the value of $x$.
So, we can simply say that $x.x=x$.

So, the correct answer is “Option A”.

Note: Here in this question we should be clear with the difference between and & or Boolean operation. From the basic concept of Boolean algebra theorems, for the “and” operation ($.$) between any two Boolean variables $A,B$, the result will be 1 if the value of both $A,B$ are 1 otherwise it will be 0 & for the “or” operation (+) between any two Boolean variables $A,B$, the result will be 1 if any one of the values of both $A,B$ is 1 otherwise it will be 0. If we by mistake take or Boolean operation instead and Boolean operation we will have the same concluding result but it is wrong according to the concept.