Suppose that the universal set U = { 1,2,3,... 20 } and that sets S and T are defined as follows: 1. %3D S = { xI x is an even integer between 3 and 11 } %3D T = {xI x is a multiple of 4 between 3 and 18 } Find: n (S) b. n (T) Crare a. n (SUT) d. n (S n T) C.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![Section 4:
Exercises
Suppose that the universal set U = { 1,2,3,... 20 } and that sets S and T
are defined as follows:
1.
S = { xI x is an even integer between 3 and 11 }
T = { xI x is a multiple of 4 between 3 and 18 }
Find:
n (S)
b.
n (T)
Cra
a.
d.
n (S N T)
c.
n (SUT)
deam ADMY 0ar eRA
Counting
2.
Using sets S and T from problem 1:
Verify that n (T') =
n(U) - n(I). dmom er lo
a.
b.
Verify that n ( SUT) = n (S) + n (T) - n(Sn T)
Suppose sets A and B are subsets of a universal set U with n (A) = 30,
n(B) = 15, and n(An B) = 6.
3.
Find n (AUB).
Suppose that R and S are subsets of some universal setU with n(U) = 50.
If n (S) = 20, n(R') = 15 and n(R n S) = 10, find n(RUS).
4.
Suppose that sets X and Y are subsets of some universal set U withn(U) = 100.
Find n (XUY) if n (X) = 30, n(Y) = 60 and n[ (X n Y)'] = 90
5.
Suppose sets P and Q are subsets of some universal set U such that n ( P) = 11,
n (Q) = 17, and n (PUQ) = 23. Find n (Pn Q).
6.
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