Discrete Mathematics Answers

How many distinct permutations are there in each word?

20. MOMMY

21. REARRANGE

22. MATHEMATICS

23. PROBABILITY

24. STATISTICS

25. PHILIPPINES

In a survey of 130 people, the following data were collected: 106 people subscribed to the newspaper, 29

people subscribed to magazines, and 17 people were members of a mail CD club. Seventeen subscribed to

both the newspaper and the magazines, 5 people subscribed to magazines and were members of a CD

club, and 10 people subscribed to the newspaper and were members of a mail CD club. Three people

subscribed to both the newspaper and magazines and were members of a mail CD club. Make and fill in a

Venn diagram to illustrate this situation

4. A survey of 100 students produced the following information: 30 speak English, 45 speak Hindi and 60 speak Marathi. It is found that 10 speak both. English and Hindi, 20 speak both Hindi and Marathi, 15 speak both English and Marathi and 5 speak all the three languages.

a) How many of these students speak none of the three languages ? b) How many of these students speak exactly two languages ?

A survey of 100 students produced the following information: 30 speak English, 45 speak Hindi and 60 speak Marathi. It is found that 10 speak both English and Hindi, 20 speak both Hindi and Marathi, 15 speak both English and Marathi and 5 speak all the three languages. a) How many of these students speak none of the three languages ? b) How many of these students speak exactly two languages ?

Identify the mapping diagram that represents the relation and determine whether the relation is a function(−3,−6),(−1,−6),(5,−6),(8,−6)

Given P(x,y) :y=x+5 ,determine the truth value of each of the following if the universe is the set of real numbers.

Determine wheter 4 is the element of each of the following sets

A: P={1,2,3,4,5}

B: R={prime numbers}

{F} Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive. b. irreflexive, symmetric, and transitive. c. irreflexive, antisymmetric, and not transitive. d. reflexive, neither symmetric nor antisymmetric, and transitive. e. neither reflexive, irreflexive, symmetric, antisymmetric, nor transitive.

{F} Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also symmetric?

{F} Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2