Discrete Mathematics Answers

1. Write the multisets of prime factors for the given numbers.

I. 160

II. 120

III. 250

2. Write the multiplicities of each element of multisets in part 2(1-I, ii,iii) separately.

3. Find the cardinalities of each multiset in part 2-1.

1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A∩B are respectively 72, 28 and 13, then find the cardinality of the set A∪B.


2. If n(A-B)=45, n(AUB )=110 and n(A∩B)=15, then find n(B).


3. If n(A)=33, n(B)=36 and n(C)=28, find n(A∪B∪C).

The binary operation on Z given by x

mathrmast (y=1+xy) not in the question later appered when i pasted)

is______ but not associative

a.Associative

b.Commutative

c.Distributive

d.Additive

Prove that n ! > 2^n for n a positive integer greater than or equal to 4.

Prove that LHS = RHS

a) Provide an example of a relation T on set A = {1, c, 3} that is irreflexive and satisfies trichotomy. (What is Trichotomy)


b) Let S= {(1, 2), (3, 4), (2, 3)} be a relation on set B = {1, 2, 3, 4}.

Is S functional? Motivate your answer


c) Let C = {1, 2, a, b} and let R = {(1, 1), (a, b), (b, 2)} and S = {(2, 1), (a, 1), (b, b), (b, 2), (2, a)} be two relations on C

i) Determine R o S (S;R)

ii) Which ordered pairs must be added to R to make it a reflexive relation?

A number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. How many students toa number of science students prepared for examination in physics, chemistry and mathematics. Out of the number 15 took physics,23 took Maths and 20 took chemistry. 6 took physics and maths, 9 took maths and chemistry. all those who took physics also took chemistry. One of the students felt ill and fail to write the exams. A. How many students took exactly one of the subjects? B. how many students took exactly two of the subjects? C. How many students prepare for the examination?

Does deductive reasoning always work? Elaborate your answer

Let A,B,C be subsets of a set. Prove that,

A ∩ B ⊆ C iff A ⊆ Bcompliment ∪ C.

In a road worthiness test on 40 cars. 60% passed. The number that failed had faults in clutch, brakes and steering as follows: Clutch only - 28; clutch and steering - 14; clutch, steering and brakes - 8; clutch and brakes - 20; brakes are steering only - 6.

The number of cars with faults in steering only is twice the number of cars with faults in brakes only.

(i) draw a Venn diagram to illustrate the information

(ii) how many cars had:

(a) Faulty breaks?

(b) Only one fault?