If X= {a,b,c,d} , Y = {f , b,d,g} , find:
(i) X-Y
(ii) Y-X.

Answer

To solve the problem, we need to find the difference between the two sets \(X\) and \(Y\).

Given:
- \(X = \{a, b, c, d\}\)
- \(Y = \{f, b, d, g\}\)

### Step-by-step Solution:

**(i) Finding \(X - Y\)**

1. **Definition**: \(X - Y\) means we take all the elements from set \(X\) and remove any elements that are also in set \(Y\).

2. **Check each element of \(X\)**:
- **Element \(a\)**:
- Is \(a\) in \(Y\)? No.
- So, include \(a\) in \(X - Y\).
- **Element \(b\)**:
- Is \(b\) in \(Y\)? Yes.
- So, do not include \(b\) in \(X - Y\).
- **Element \(c\)**:
- Is \(c\) in \(Y\)? No.
- So, include \(c\) in \(X - Y\).
- **Element \(d\)**:
- Is \(d\) in \(Y\)? Yes.
- So, do not include \(d\) in \(X - Y\).

3. **Result**:
- After checking all elements, we find that \(X - Y = \{a, c\}\).

**(ii) Finding \(Y - X\)**

1. **Definition**: \(Y - X\) means we take all the elements from set \(Y\) and remove any elements that are also in set \(X\).

2. **Check each element of \(Y\)**:
- **Element \(f\)**:
- Is \(f\) in \(X\)? No.
- So, include \(f\) in \(Y - X\).
- **Element \(b\)**:
- Is \(b\) in \(X\)? Yes.
- So, do not include \(b\) in \(Y - X\).
- **Element \(d\)**:
- Is \(d\) in \(X\)? Yes.
- So, do not include \(d\) in \(Y - X\).
- **Element \(g\)**:
- Is \(g\) in \(X\)? No.
- So, include \(g\) in \(Y - X\).

3. **Result**:
- After checking all elements, we find that \(Y - X = \{f, g\}\).

### Final Answers:
- \(X - Y = \{a, c\}\)
- \(Y - X = \{f, g\}\)