How Do Graph Relations and Predicates Work in Discrete Math?

[confusedgal]

Hi :)

I have my Discrete maths final in 2 days, and I was doing some practice questions and came across 2 parts that completely baffled me - I moved onto my course a bit late so I missed chunks from classes.

please please please, can you explain them to me? I've put the questions in pictures, they're attached :).

Ive read on the different types of relations, but its like gibberish. Can someone please simplify them? please?

http://img340.imageshack.us/img340/7435/predicatesfp6.jpg
http://img517.imageshack.us/img517/315/graphrelationssk7.jpg

 

[EnumaElish]

For the graphs, can you state the definitions of reflexive, transitive, and (anti)symmetric that you are supposed to use?

For the predicates, what does a large dot mean? What does ":" mean?

 

[tacman]

Hi there!

Firstly, let's define what a relation and a predicate are.

A relation is a set of ordered pairs, where the first element is called the input or domain, and the second element is called the output or range. It is a way to show how elements from one set are related to elements of another set. For example, the relation {(1,2), (3,4), (5,6)} shows that 1 is related to 2, 3 is related to 4, and 5 is related to 6.

A predicate is a statement that can be either true or false, depending on the values of its variables. It is used to describe properties or characteristics of objects or elements in a set. For example, the predicate "x is an even number" is true for all even numbers and false for all odd numbers.

Now, let's look at the first question about predicates. In this question, we are given a set of elements and a predicate, and we are asked to determine which elements satisfy the predicate. So, for example, in the first part, the predicate is "x is a multiple of 3", and the set of elements is {1, 2, 3, 4, 5, 6}. To solve this, we go through each element in the set and check if it satisfies the predicate. In this case, only 3 and 6 satisfy the predicate, so the answer is {3, 6}.

Now, let's move on to the second question about graph relations. In this question, we are given a graph and we are asked to determine the relation it represents. The graph shows the relationship between two sets, where the elements on the left side are the domain and the elements on the right side are the range. So, for example, in the first part, we can see that 1 is related to 2, 3 is related to 4, and 5 is related to 6, which matches the relation we saw earlier: {(1,2), (3,4), (5,6)}.

I hope this helps to clarify things for you. If you have any other questions, feel free to ask. Good luck on your exam!