Discrete Mathematics Answers

Determine the number of subsets of size k of the set {1, 2, . . . , n} which do not contain consecutive integers. For instance, when n = 4 and k = 2, there are 3 such subsets, namely {1, 3}, {1, 4} and {2, 4}. 

Let S be the following ordered sequence of elements S = {1, 2, 3, 4, 5, 6} and the universal set U be {1, 2, 3, 4, 5, 6}.

Write down the characteristic vectors of

• A = {1, 2, 4, 5};

• B = {3, 5};

• ∅;

• A ∪ B;

• A ∩ B;

• A∪ ∼ B;

• A∆B.

If

n fairsix-sided dice are tossed and the numbers showing on top are recorded, how many

(a) record sequences are possible?

(b) sequence contain exactly one six?

(c) sequences contain exactly four twos, assuming

n ≥ 4?

There are 4 adults and 6 children sitting around a round table. If there must be at least one child 

between any two adults, then how many ways are there for them to sit around the table? Rotations are 

considered the same, while reflections are distinct.

Use deductive reasoning to show that the following procedure always produces a number that is equal to the original number.

Procedure: Pick a number. Multiply the number by 6 and add 8.

Divide the sum by 2, subtract twice the original number,

and subtract 4.

Use Polya’s four-step problem-solving strategy and the problem-

solving procedures to solve each of the following exercises.

(a) An android phone and a Bluetooth speaker together cost Php6500.00

. The phone costs Php2000.00 more than the speaker. What is

the cost of the phone?

(b) In how many ways can you answer a 12-question true-false test

if you answer each question with either a “true” or a “false”?

(c) A total of 364 first-year students of CMU are currently enrolled

in the subject GEC14. If there are 26 more girls than boys, how

many girls are there?

Find all the minimal and maximal elements of A= {2 ,3 ,4 ,6 ,8 ,24 ,48} with

partial order of divisibility using Hasse diagram