Help with char

hello i have a problem i need to compare char. It doesnt work. Can you help me??

char A[10]="101001010";
char x[0];
char y[]="1";
char z[]="0";
int i;

void setup() {
   
   Serial.begin(9600);
  
  

}

void loop() {
for(i=0; i<sizeof(A)-1;i++){
  x[0]=(A[i]);
  Serial.write (x[0]);
  if (strcmp (x,y) == 0)
  { Serial.write ("true");
  Serial.println( );}
  if (strcmp (x,z) == 0)
  { Serial.write ("false");
  Serial.println( );}
   

delay (1000);}

What is your intended logic? Give us some sample input and outputs. The program is horribly written. It's like every line has a mistake. I'll pick out one at a time:
Use Serial.print instead of write when you try to output "true" or "false".

char x[0];

You are trying to store a character into an array that can hold at most ZERO characters.

 x[0]=(A[i]);
  if (strcmp (x,y) == 0)

You are storing a single character into an array and treating it as a null-terminated string without inserting a null terminator.

It looks like what you are trying to do is:

char A[] = "101001010";  // Safer not to force the array size

void setup() {
  Serial.begin(9600);
}

void loop() {
  for (unsigned int i = 0; i < strlen(A); i++) {
    // You don't have to store each element in a variable to
    // display or compare.
    Serial.write(A[i]);
    if (A[i] == '1') {  // You can directly compare characters
      Serial.println(" true");
    }
    else if (A[i] == '0') {
      Serial.println(" false");
    }
    delay (1000);
  }
}

I think the problem was that you knew how to compare character strings (strcmp()) but did not know you can compare individual characters just like any other integers.