In the following , state whether A=B or not :
(i) A = {a,b,c,d}, B= {d,c,b,a}
(ii) A= {4,8,12,16},B= {8,4,16,18}.
(iii) A={2,4,6,8,10},
B=x:x is a positive even integer and `xle10}`
(iv) A= {x:x is multiple of 10},
B= {10,15,20,25,30,.....}.

Answer

To determine whether the sets A and B are equal, we need to check if they contain the same elements. Two sets are considered equal if they have exactly the same elements, regardless of the order in which they are listed.

Let's analyze each part step by step:

### Part (i)
- **Given Sets:**
- A = {a, b, c, d}
- B = {d, c, b, a}

**Step 1:** Count the elements in both sets.
- Set A has 4 elements: a, b, c, d.
- Set B has 4 elements: d, c, b, a.

**Step 2:** Check if the elements are the same.
- Both sets contain the same elements: a, b, c, d.

**Conclusion:** Since both sets have the same elements, A = B.

### Part (ii)
- **Given Sets:**
- A = {4, 8, 12, 16}
- B = {8, 4, 16, 18}

**Step 1:** Count the elements in both sets.
- Set A has 4 elements: 4, 8, 12, 16.
- Set B has 4 elements: 8, 4, 16, 18.

**Step 2:** Check if the elements are the same.
- Set A contains 12, which is not in Set B.
- Set B contains 18, which is not in Set A.

**Conclusion:** Since the elements are not the same, A ≠ B.

### Part (iii)
- **Given Sets:**
- A = {2, 4, 6, 8, 10}
- B = {x : x is a positive even integer and x ≤ 10}

**Step 1:** Identify the elements of Set B.
- The positive even integers less than or equal to 10 are: 2, 4, 6, 8, 10.

**Step 2:** Compare the elements of both sets.
- Set A = {2, 4, 6, 8, 10}
- Set B = {2, 4, 6, 8, 10}

**Conclusion:** Since both sets have the same elements, A = B.

### Part (iv)
- **Given Sets:**
- A = {x : x is a multiple of 10}
- B = {10, 15, 20, 25, 30, ...}

**Step 1:** Identify the elements of Set A.
- Set A includes all multiples of 10: 10, 20, 30, 40, ...

**Step 2:** Compare the elements of both sets.
- Set A includes: 10, 20, 30, 40, ...
- Set B includes: 10, 15, 20, 25, 30, ...

**Step 3:** Check for common elements.
- Set B contains 15 and 25, which are not multiples of 10.

**Conclusion:** Since the elements are not the same, A ≠ B.

### Final Summary:
- (i) A = B
- (ii) A ≠ B
- (iii) A = B
- (iv) A ≠ B