Discrete Mathematics Answers

1. In a certain examination, 72 candidates offered Maths, 64 offered English, 62 offered French, 18 offered both Maths and English, 24 offered Maths and French, and 20 offered English and French. While 8 candidates offered all the three subjects. How many candidates were there for the examination?

Find in set builder notation the set of all positive integers a such that

a≡137 (mod 5).

A car number plate consists of a letter, followed by five numbers, and ended with three letters. How many car number plates can be formed? if required there must not be the same letter and no equal lift, and how many car number plates can be formed ?

The fibonacci sequence is defined as x0 = 0, x1 = 1 and xn+2 = xn +xn+1 , for all non negative integers n prove that, xm = xr+1xm-r + xrxm-r for all integers m ≥ 1 and 0 ≤ r ≤ m-1 and xd divides xkd for all integers k and d

The fibonacci sequence is defined as x0 = 0, x1 = 1 and xn+2 = xn +xn+1 , for all non negative integers n prove that, xm = xr+1xm-r + xrxm-r for all integers m ≥ 1 and 0 ≤ r ≤ m-1 and xd divides xkd for all integers k and d

Please read the following behavioral objective and identify the parts of the objectives as asked in the following questions.On the bus, Jonathan will sit quietly for 20 minutes, 80% of the time over 5 sessions.Choose the portion of the sentence that is the “what” condition.


A.

“will sit quietly”

B.

“on the bus”

C.

“Jonathan”

D.

“80% of the time over 5 sessions”

Chin-Tan found 52 action figures for his yard sale.

He wants to put them in more than 1 box, but fewer than 5 boxes.

Each box will have the same number of figures.

How many boxes can Chin-Tan use? Explain.

3. Stella Maris Schools, at one time, has 37 vacancies for teachers, out of which 22 are for English Language, 20 for History, 17 for Fine-Art. Of these vacancies, 11 are for both English Language and History, 8 for both, History and Fine Art, 7 for English Language and Fine-Art.

Using a Venn diagram or otherwise, find the number of teachers who must be able to teach:

a. All the three subjects.

b. Fine Art only

c. English Language and History not Fine Art.

Let A and B be finite sets for which |A|=|B| and suppose f: A —> B. Prove that f is injective if and only if f is surjective

b) Suppose that b is small and d is large, and further that either b and d are identical or that c is a

tetrahedron. Max believes that c must be a tetrahedron on the basis of this information. Which of

the following is true of this situation?


1. Max is correct to believe that we can determine the shape of c but it is not a tetrahedron,

since the given information is contradictory.

2. Max is mistaken, and nothing can be concluded about c, after all c is only mentioned in

one of the disjuncts of a disjunction.

3. Max is correct, because there is no situation in which b is small, d is large and b and d are

names of the same objects.

4. Max is correct, because it there is no situation in which b is small, d is large, and c is a

cube.