Discrete Mathematics Answers

Write CONVERSE of the following statements.

a)If P is a square, then P is a rectangle.

b)If n is prime, then n is odd or n is 2.

c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt.

d)A positive integer is prime only if it has no divisors other than 1 and itself.

e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.

Write NEGATION of the following statements (Careful, NEGATION is not the same as INVERSE)

a)If P is a square, then P is a rectangle.

b)If n is prime, then n i odd or n is 2.

c)If Aangloo is Meena's father, then Baangloo is her uncle and Bingli is her Aunt.

d)A positive integer is prime only if it has no divisors other than 1 and itself.

e)Being divisible by 3 is a necessary condition for this number to be divisible by 9.

How many cards must be selected from a standard deck of 52 cards to guarantee that at least 5 spades are selected? 

Suppose f:X→Y and g:Y→Z and both of these are one-to-one and onto. Prove that (g∘f)^(-1) exists and that (g∘f)^(-1)=f^(-1)∘g^(-1).

There are 70 women in class. Each play at least one game of the following games; volleyball, basketball, table tennis.

20 play volleyball only,10 play basketball only and 6 play table tennis.

4 play all the games and an equal number play 2 games only.

A) Illustration these informations on a Vern diagram.

i) Find the number of women who play volleyball.

Check whether the relation R ={(x, y)∈N×N | xy is the square of an integer} is an equivalence relation on N.

2 Draw a Venn diagram of set A, B, C where

(i) A and B have elements in common, B and C have element in common but A and C are disjoint.

1. Let A = {a,b,c}, B = {x,y}, and C = {0,1}. Find
2. a) A×B×C. 

1. a) thesetofpeoplewhospeakEnglish,thesetofpeople
2. who speak English with an Australian accent 

There were 100 students in the library who responded to how they completed their research papers.

• 18 students only used the periodicals.

• 29 students used the web and books.

• 15 students used books, the web, and periodicals.

• 40 students used books and periodicals.

• 20 used the web and periodicals.

• 60 students used books.

• 7 students did not use the web, nor books, nor periodicals.

a) Represent this information with a Venn diagram.

b) How many students only used the web in their research?

c) How many students used books or periodicals?