Help with this problems please? 1. Give an example of a subset S of the set of all the subsets of N={a,b,c,d,e}, such that | S= 4and the partial order relation R on S, defined by c, is a total order on S.2. Suppose an airline has 7 pilots (A, B, C, D, E, F, G) and it serves 4 destinations (W, X, Y, Z).How many different assignments (one pilot per flight) are possible, if pilot A cannot fly to destination W,where one will get arrested.3. Suppose a universal set 2={0,1,2,..,9}. Give an example of sets A, B, and C, whereA-C = B-C, yet A±B.4. Simplify (A- B)O(B- A), where A and B are sets, subsets of a universal set N.5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}.Define a relation R on S as follows: AR B if AOB±Ø.Is R an equivalence relation? Completelyjustify your answer.6. Let S be the set of the subsets of 2= {1,2, 3, 4} . Define a relation Ron S as follows:For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relationon S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all theelements in each class. Note, the result of your work can be viewed as describing the partition Pof theset S, induced by the relation R.7. We are returning to the members of the Club from the last HWK. Suppose the management decidedto use, to rank the members, a relation R on the set of members, defined as follows:Let A and B be two members, then A R Bif either A belonged to the club at least as many years as B orA's contribution is at least as large as that of B.Is R, as defined above, a partial ordering? Explain.8. Let f:Z→Z be a function, mapping from the set of integers to the set of integers, defined asfollows f(n) = 3n +1. Is ƒ one-to-one? Is it onto?9. How many distinct functions mapping from set X= {a,b,c,d} onto set Y = {1,2} are there?

Name: Help with this problems please? 1. Give an example of a subset S of th
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Description: Help with this problems please? 1. Give an example of a subset S of the set of all the subsets of N={a,b,c,d,e}, such that | S= 4and the partial order relation R on S, defined by c, is a total order on S.2. Suppose an airline has 7 pilots (A, B, C, D