Practice Number Of Binary Relations (16.2.3) - Relations - Discrete Mathematics

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6 sample questions

Question 1.
Define a binary relation based on the sets A = {1, 2} and B = {a, b}.
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Use pairs of elements from each set.
Question 2.
How many elements are in the Cartesian product of A = {1, 2} and B = {a, b, c}?
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Multiply the number of elements in set A by those in set B.
3Question 3.
What is a binary relation?
- A set of ordered pairs
- A single element
- A sub-collection of elements
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Think about the definition involving ordered pairs.
4Question 4.
True or False: The empty relation is a valid binary relation.
- True
- False
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Consider if an empty set can make a relation.
Question 5.
Given two sets A = {x, y} and B = {1, 2, 3}, find all possible binary relations, and compute the total count. Discuss the nature of the relations.
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Examine subsets of the Cartesian product A x B.
Question 6.
Consider the relation defined over A = {1, 2, ..., 5} such that aRb if and only if a is less than b. List all pairs and construct the corresponding Boolean matrix.
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Use ordered pairs, and for the matrix, remember positions for true pairs.

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