Relation And Functions

Question 1

What is a reflexive relation?

Answer 1

A relation R in a set A is called reflexive if, for every a in A, (a, a) is in R.

Question 2

What defines a symmetric relation?

Answer 2

A relation R in a set A is called symmetric if, for every a, b in A, (a, b) is in R implies (b, a) is also in R.

Question 3

Define a transitive relation.

Answer 3

A relation R in a set A is called transitive if, for every a, b, c in A, (a, b) is in R and (b, c) is in R implies (a, c) is in R.

Question 4

What is an equivalence relation?

Answer 4

A relation R in a set A is said to be an equivalence relation if it is reflexive, symmetric, and transitive.

Question 5

What characterizes a one-one function?

Answer 5

A function f:X→Y is one-one if for every x1, x2 in X, f(x1) = f(x2) implies x1 = x2.

Question 6

How is an onto function defined?

Answer 6

A function f:A→B is onto if for every y in B, there exists an element x in A such that f(x) = y.

Question 7

What is the relationship between range and co-domain in an onto function?

Answer 7

In an onto function, the range is equal to the co-domain.

Question 8

What is a composite function?

Answer 8

A composite function f: A → B and g: B → C is defined as g(f(x)).

Question 9

Fill in the blank: A relation R in a set A is called ______ if for every a, b, c in A, (a, b) is in R and (b, c) is in R implies (a, c) is in R.

Answer 9

transitive relation

Question 10

True or False: An equivalence relation must be reflexive.

Answer 10

True

Question 11

True or False: A one-one function can have multiple elements in the domain mapping to the same element in the co-domain.

Answer 11

False