I DID PART a I NEED THE SOLUTION FOR THE OTHER PARTS AND PRO

I DID PART (a) I NEED THE SOLUTION FOR THE OTHER PARTS AND PROBLEM 6

Problem 4 [Set operations] A and B are sets of integers, A-(-6,-4,-0.5, 0, 1.6, 8} and B = {-0.5, 0, 1, 2, 4} (a) Find the following sets (iii) AUIB iii AB (iv) AnlB (b) Suppose that AUB S, meaning that each element in S is contained in A, or B, or both. Find (AnB)c (c) Determine where AC Bor A 2 B (d) Determine where A and B are mutually-exclusive sets. Problem 5 |Set concepts: DeMorgan\'s laws| \"Prove\" DeMorgan\'s laws using Venn diagrams. Problem 6 |Uniform probability] How do we assign probabilities in a random experiment? From a strictly (complement)

Solution

b) AUB is a sample space therefore AUB = { -6,-4,-0.5,0,1,1.6,2,4,8}

AnB = {0,-0.5}

(AnB)^c = Sample space - (AnB) = { -6,-4,1,1.6,2,4,8}

c) Neither A is a subset of B nor B is a subset of A as non of the set is contained in another completely

d) as (AnB) is not null therefore A and B are not mutually exclusive

Problem 5) Demorgan\'s law = P(AnB)^c = P(A^c U B^c )

6) In a random experiment as outcomes are not know in advance and S denotes the sample space of all possible outcomes so to each element of S we assign an uniform probability of occuring which is 1/ no. of elements in S

As in rolling a die the probability of any number between 1 to 6 occuring is 1/6 as there are 6 possible outcomes

2. While tossing a coin probability of occuring a head or tail is 1/2