Discrete Mathematics Answers

Question 3

Let G and L be relations on A = {1, 2, 3, 4} with

G = {(1, 2), (2, 3), (4, 3)} and L = {(2, 2), (1, 3), (3, 4)}.

Which one of the following alternatives represents the relation L ￮ G = G; L?

1. {(2, 3), (3, 3)}

2. {(1, 2), (2, 4), (4, 4)}

3. {(1, 2), (2, 1), (3, 3), (4, 4)}

4. {(2, 4), (4, 4)}

Suppose U = {1, 2, 3, 4, 5, a, b, c} is a universal set with the subset A = {a, b, c, 1, 2, 3, 4}.

Answer questions 1 and 2 by using the given sets U and A.

Question 1

Which one of the following relations on A is NOT functional?

1. {(1, 3), (b, 3), (1, 4), (b, 2), (c, 2)}

2. {(a, c), (b, c), (c, b), (1, 3), (2, 3), (3, a)}

3. {(a, a), (c, c), (2, 2), (3, 3), (4, 4)}

4. {(a, c), (b, c), (1, 3), (3, 3)}

Question 2

Which one of the following alternatives represents a surjective function from U to A?

1. {(1, 4), (2, b), (3, 3), (4, 3), (5, a), (a, c), (b, 1), (c, b)}

2. {(a, 1), (b, 2), (c, a), (1, 4), (2, b), (3, 3), (4, c)}

3. {(1, a), (2, c), (3, b), (4, 1), (a, c), (b, 2), (c, 3)}

4. {(1, a), (2, b), (3, 4), (4, 3), (5, c), (a, a), (b, 1), (c, 2)}

What is 10001000₂ - 0001101100₂

a)          Freddie has 6 toys cars and 3 toy buses, all different. 

i)              Freddie arranges these 9 toys in a line. Find the number of possible arrangements 

·           if there is a car at each end of the line and no buses are next to each other.

a)          Freddie has 6 toys cars and 3 toy buses, all different. 

i)              Freddie arranges these 9 toys in a line. Find the number of possible arrangements 

if the buses are all next to each other.

A fair six-sided dice is thrown and the scores are noted.

Event X: The total of the two scores is 4.

Even Y: The first score is 2 or 5.

a)              Construct the table by showing the sample spaces.                                          

a)              Write each statement in symbolic form using p, q and r.

If I study, then I will not fail mathematics.

If I do not play basketball, then I will study.

But I failed mathematics.

Then, test the validity of the following argument by using the truth table.

Show that a fuzzy relation R on a set U is anti-symmetric if and only if each of its alpha-cuts is an anti-symmettric relation on U

Every function is a relation, but the converse is not true.”--True or false? Justify with an example.