Mathematics Relations Quiz

What is a relation in mathematics?

• A function that maps one set to another

• A subset of the Cartesian product of two sets

• A set of ordered pairs where each element is unique

• A combination of sets and subsets

If A={1,2} and B={x,y}, what is the Cartesian product A×B?

• {(1,x),(2,y)}

• {(1,x),(1,y),(2,x),(2,y)}

• {(x,1),(y,2)}

• {(x,y)}

A relation is called symmetric if:

• (a,b)∈R⇒(b,a)∈R

• (a,b)∈R⇒(a,a)∈R

• (a,b)∈R⇒(b,a)∉R

• (a,b)∈R⇒(b,c)∈R

A relation is called transitive if:

• (a,b),(b,c)∈R⇒(a,c)∈R

• (a,b)∈R⇒(b,a)∈R

• (a,b)∈R⇒(a,a)∈R

• (a,b)∈R⇒(b,c)∉R

What is a reflexive relation?

• Every element is related to itself

• No element is related to itself

• Only one element is related to itself

• None of the above

Given A={1,2,3}, which of the following is a reflexive relation?

• {(1,1),(2,2),(3,3)}

• {(1,2),(2,3)}

• {(1,1),(2,2)}

• {(1,2),(2,3),(3,1)}

Which of the following is NOT a property of equivalence relations?

• Reflexive

• Symmetric

• Transitive

• Antisymmetric

What is an equivalence relation?

• A relation that is reflexive, symmetric, and transitive

• A relation that is only reflexive

• A relation that is reflexive and transitive

• A relation that is symmetric and antisymmetric

If A={1,2,3}, what is the number of possible relations on A?

• 9

• 16

• 8

• 64

A relation that is antisymmetric must satisfy which of the following?

• (a,b)∈R⇒(b,a)∈R

• (a,b)∈R⇒(b,a)∉R unless a=b

• (a,b)∈R⇒(a,a)∈R

• None of the above