Given X={a,b,c,d,e} and Y={a.c.e}, find the compliment of Y in X
1 {b,d}
2 {a,b,c,d,e}
3 {a,c,e}
4 {}
To find the complement of Y in X, we need to identify the elements in X that do not belong to Y.
Y = {a, c, e} is given as a subset of X = {a, b, c, d, e}.
The complement of Y in X, denoted as X' or X\Y, represents the elements in X that are not present in Y. Therefore, we need to find the elements in X that are not in Y.
To do this, we can compare each element of X with each element of Y and exclude the ones that are present in Y.
Let's go through the process step by step:
1. Start with the given sets:
X = {a, b, c, d, e} and Y = {a, c, e}.
2. Compare each element in X with each element in Y:
- 'a' is present in both X and Y.
- 'b' is not present in Y.
- 'c' is present in Y.
- 'd' is not present in Y.
- 'e' is present in Y.
3. Exclude the elements from X that are present in Y:
Exclude 'a', 'c', and 'e' from X.
4. The remaining elements in X are the complement of Y:
The complement of Y in X is {b, d}.
Therefore, the correct answer is option 1: {b, d} is the complement of Y in X.