Given that E=(All the letter of the alphabet)
X=(A,E,I,O,U)
Y=(E,D,C,D,F,H)
Find
XnY' and (XnY)
Y' is all the letters except those in Y, so
X∩Y' = {A,I,O,U)
X∩Y = {E}
and why does Y have D twice?
To find XnY', first, we need to find the complement of Y. The complement of Y, denoted as Y', includes all the elements that are in the universal set (E) but not in Y.
Y' = E - Y
= (All the letters of the alphabet) - (E, D, C, D, F, H)
= A, B, G, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z
Next, we find the intersection of X and Y'. The intersection, denoted by XnY', includes all the elements that are common to both X and Y'.
XnY' = X ∩ Y'
= (A, E, I, O, U) ∩ (A, B, G, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z)
= A, I, O, U
Now, let's find the intersection of X and Y, denoted by XnY. This includes all the elements that are common to both X and Y.
XnY = X ∩ Y
= (A, E, I, O, U) ∩ (E, D, C, D, F, H)
= E
Therefore, XnY' is {A, I, O, U}, and XnY is {E}.