Discrete Mathematics Answers

Determine whether the relation R

on the set of all integers is reflexive,

symmetric, antisymmetric, and/or

transitive, where (x, y)=R if and

only if

X=Y²

How many bijections (bijective functions) are there from A to A with the

property that no element of A is mapped to itself? (A is a set with 5 elements)

Verify that each of the following statements is a false statement by finding a counterexample for each.

1. xx=1
2. x+33=x+1
3. x2+16=x+4

Wanda, Loki, Natasha, and Stephen were recently elected as the new class officers (president, vice

president, secretary, treasurer) of the sophomore class at Marvel College. From the following clues,

determine which position each holds.

1. Stephen is younger than the president but older than the treasurer.

2. Wanda and the secretary are both the same age, and they are the youngest members of the

group.

3. Natasha and the secretary are next door neighbors.

Determine whether each of the following arguments is an example of inductive reasoning or deductive

reasoning.

a. All Janet Evanovich novels are worth reading. The novel To the Nines is a Janet Evanovich

novel. Thus To the Nines is worth reading.

b. I know I will win a jackpot on this slot machine in the next 10 tries, because it has not paid out

any money during the last 45 tries.

Use deductive reasoning to show that the following procedure produces a number that is three times

the original number. Procedure: Pick a number. Multiply the number by 6, add 10 to the product, divide

the sum by 2, and subtract 5. Hint: Let n represent the original number.

Use inductive reasoning to predict the most probable next number in the following lists.

a) 5, 10, 15, 20, 25, ?

b) 2, 5, 10, 17, 26, ?

Consider the following procedure: Pick a number. Multiply the number by 9, add 15 to the product,

divide the sum by 3, and subtract 5. Complete the above procedure for several different numbers. Use

inductive reasoning to make a conjecture about the relationship between the size of the resulting number

and the size of the original number.

. State the converse, contrapositive, and inverse of each of these conditional statements. A positive integer is a prime only if it has no divisors other than 1 and itself.

What is the number of subsets of a set with n elements, containing a given element (when element becomes fixed, part of every subset)?