Find the sets which are equal, from the following sets :
`A = {2,1,3}`
`B = {x : x^(3) - 6x^(2)+11x - 6 = 0}`
`C = {0,1},D={a,b}`
`E = {x : x^(2) - x=0}`
`F = {x : (x-a)(x-b)=0}`.

Answer

To determine which sets are equal from the given sets, we will analyze each set and find their elements.

### Step 1: Identify the elements in set A
Set A is given as:
\[ A = \{2, 1, 3\} \]
The elements in set A are 1, 2, and 3.

### Step 2: Solve the equation for set B
Set B is defined as:
\[ B = \{x : x^3 - 6x^2 + 11x - 6 = 0\} \]
To find the roots of this cubic equation, we can factor it or use synthetic division. The roots of the polynomial can be found to be:
- \( x = 1 \)
- \( x = 2 \)
- \( x = 3 \)

Thus, we can write:
\[ B = \{1, 2, 3\} \]

### Step 3: Compare sets A and B
Now we compare sets A and B:
\[ A = \{2, 1, 3\} \]
\[ B = \{1, 2, 3\} \]
Since both sets contain the same elements, we conclude:
\[ A = B \]

### Step 4: Identify the elements in set C
Set C is given as:
\[ C = \{0, 1\} \]
The elements in set C are 0 and 1.

### Step 5: Identify the elements in set D
Set D is given as:
\[ D = \{a, b\} \]
The elements in set D are a and b.

### Step 6: Compare sets C and D
Sets C and D have different elements, so:
\[ C \neq D \]

### Step 7: Solve the equation for set E
Set E is defined as:
\[ E = \{x : x^2 - x = 0\} \]
Factoring gives:
\[ x(x - 1) = 0 \]
The roots are:
- \( x = 0 \)
- \( x = 1 \)

Thus, we can write:
\[ E = \{0, 1\} \]

### Step 8: Compare sets C and E
Now we compare sets C and E:
\[ C = \{0, 1\} \]
\[ E = \{0, 1\} \]
Since both sets contain the same elements, we conclude:
\[ C = E \]

### Step 9: Solve the equation for set F
Set F is defined as:
\[ F = \{x : (x - a)(x - b) = 0\} \]
The roots of this equation are:
- \( x = a \)
- \( x = b \)

Thus, we can write:
\[ F = \{a, b\} \]

### Step 10: Compare sets D and F
Now we compare sets D and F:
\[ D = \{a, b\} \]
\[ F = \{a, b\} \]
Since both sets contain the same elements, we conclude:
\[ D = F \]

### Final Conclusion
The equal sets are:
- \( A = B \)
- \( C = E \)
- \( D = F \)