From the sets given below , select equal sets and equivalent sets:
A={0,a},
B= {1,2,3,4},
C={4,8,12},
D={3,1,2,4},
E= {1,0},
F={8,4,12},
G={1,5,7,11} , H= {a,b} .

Answer

To determine the equal and equivalent sets from the given sets, we will follow these steps:

### Step 1: Understand the Definitions
- **Equal Sets**: Two sets are equal if they contain exactly the same elements, regardless of the order.
- **Equivalent Sets**: Two sets are equivalent if they have the same number of elements, but the elements themselves do not have to be the same.

### Step 2: List the Sets
Given sets are:
- A = {0, a}
- B = {1, 2, 3, 4}
- C = {4, 8, 12}
- D = {3, 1, 2, 4}
- E = {1, 0}
- F = {8, 4, 12}
- G = {1, 5, 7, 11}
- H = {a, b}

### Step 3: Count the Elements in Each Set
- Set A has 2 elements: {0, a}
- Set B has 4 elements: {1, 2, 3, 4}
- Set C has 3 elements: {4, 8, 12}
- Set D has 4 elements: {3, 1, 2, 4}
- Set E has 2 elements: {1, 0}
- Set F has 3 elements: {8, 4, 12}
- Set G has 4 elements: {1, 5, 7, 11}
- Set H has 2 elements: {a, b}

### Step 4: Identify Equivalent Sets
Now, we will identify which sets have the same number of elements:
- A (2 elements) is equivalent to E (2 elements) and H (2 elements).
- B (4 elements) is equivalent to D (4 elements) and G (4 elements).
- C (3 elements) is equivalent to F (3 elements).

Thus, the equivalent sets are:
- A, E, H (each has 2 elements)
- B, D, G (each has 4 elements)
- C, F (each has 3 elements)

### Step 5: Identify Equal Sets
Next, we will check for equal sets by comparing the elements:
- Set B = {1, 2, 3, 4} and Set D = {3, 1, 2, 4} are equal because they contain the same elements.
- Set C = {4, 8, 12} and Set F = {8, 4, 12} are equal because they contain the same elements.

Thus, the equal sets are:
- B = D
- C = F

### Final Results
- **Equal Sets**: B = D, C = F
- **Equivalent Sets**: A, E, H; B, D, G; C, F