3 questions if you can help me.
1. Calculate the number of subsets and the number of proper subsets for the set.
{x|x is a day of the week}
2. Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
(A �¿ B) (A �¿ C)
See:
http://www.jiskha.com/display.cgi?id=1307635195
1. To calculate the number of subsets and proper subsets for the set {x|x is a day of the week}, we can use the formula 2^n, where n is the number of elements in the set. In this case, there are 7 days of the week.
Number of subsets:
Since there are 7 elements in the set, there will be 2^7 = 128 subsets in total. This includes the empty set and the set itself.
Number of proper subsets:
To calculate the number of proper subsets, we subtract the empty set and the set itself from the total number of subsets. So the number of proper subsets in this case is 128 - 2 = 126.
2. Let's evaluate the expressions (A �¿ B) and (A �¿ C) using the given sets.
(A �¿ B) represents the intersection of sets A and B, which means finding the elements that are common to both sets.
Set A = {q, s, u, w, y}
Set B = {q, s, y, z}
(A �¿ B) = {q, s, y} - These are the elements that are common to both sets A and B.
Set C = {v, w, x, y, z}
(A �¿ C) = { }
Since there are no common elements between sets A and C, the intersection (A �¿ C) is an empty set.