Podcast
Questions and Answers
Explain why the relation R = {(x, y) : 3x − y = 0} is not reflexive on the set A = {1, 2, 3 … 13, 14}.
Explain why the relation R = {(x, y) : 3x − y = 0} is not reflexive on the set A = {1, 2, 3 … 13, 14}.
The relation R is not reflexive because for a relation to be reflexive, it must contain all pairs (a, a) where a is an element of the set. In this case, R does not contain pairs like (1, 1), (2, 2) ... (14, 14), so it is not reflexive.
Why is the relation R = {(x, y) : 3x − y = 0} not symmetric?
Why is the relation R = {(x, y) : 3x − y = 0} not symmetric?
The relation R is not symmetric because although (1, 3) is in R, (3, 1) is not in R. For a relation to be symmetric, if (a, b) is in R, then (b, a) must also be in R, which is not the case here.
Explain why the relation R = {(x, y) : 3x − y = 0} is not transitive.
Explain why the relation R = {(x, y) : 3x − y = 0} is not transitive.
The relation R is not transitive because although (1, 3) and (3, 9) are in R, (1, 9) is not in R. For a relation to be transitive, if (a, b) and (b, c) are in R, then (a, c) must also be in R, which is not the case here.
Determine whether the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers is reflexive, symmetric, and transitive.
Determine whether the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers is reflexive, symmetric, and transitive.
State whether the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers is reflexive, symmetric, or transitive, and provide a brief explanation.
State whether the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers is reflexive, symmetric, or transitive, and provide a brief explanation.
Match the following properties with their definitions in relation to sets:
Match the following properties with their definitions in relation to sets:
Match the following terms with their definitions related to relations and sets:
Match the following terms with their definitions related to relations and sets:
Match the following examples with their respective properties in relation to sets:
Match the following examples with their respective properties in relation to sets:
Match the following terms with their relevant applications in programming:
Match the following terms with their relevant applications in programming:
Match the following relations with their corresponding properties:
Match the following relations with their corresponding properties:
Which of the following best describes the relation R = {(x, y) : 3x − y = 0} on the set A = {1, 2, 3 … 13, 14}?
Which of the following best describes the relation R = {(x, y) : 3x − y = 0} on the set A = {1, 2, 3 … 13, 14}?
In the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers, which property is violated?
In the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers, which property is violated?
Why is the relation R = {(x, y) : y = x + 5 and x < 4} not reflexive?
Why is the relation R = {(x, y) : y = x + 5 and x < 4} not reflexive?
In the set A = {1, 2, 3 … 13, 14}, why is the relation R = {(x, y) : 3x − y = 0} not transitive?
In the set A = {1, 2, 3 … 13, 14}, why is the relation R = {(x, y) : 3x − y = 0} not transitive?
Which property is violated by the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers?
Which property is violated by the relation R = {(x, y) : y = x + 5 and x < 4} on the set of natural numbers?
