Sets, Relations and Functions

Gap-fill exercise

  
Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!
A is a well-defined collection of objects.

A set which does not contain any element is called .

A set which consists of a definite number of elements is called ,otherwise, the set is called .

A set A is said to be of a set B, if every element of A is also an element of B. Intervals are subsets of R.

A power set of a set A is collection of all of A

Sets are used to define the concepts of .

The study of geometry, sequences, probability, etc. requires the knowledge of .

The interval which contains the end points also is called .

Let a, b ∈ R and a < b. Then the set of real numbers { y : a < y < b} is called an .

Most of the relationships between sets can be represented by means of diagrams which are known as .

The universal set is represented usually by a and its subsets by .

The symbol ‘∪’ is used to denote the .

The symbol ‘∩’ is used to denote the .

If A and B are two sets such that A ∩ B = φ, then A and B are called .

Let U be the universal set and A a subset of U. Then the of A is the set of all elements of U which are not the elements of A.

The function f : R → R defined by f(x) = ax + b where a≠ 0 and b are constants, is called a . A function which is not linear is called a .

A relation R in a set A is called , if each element of A is related to every element of A, i.e., R = A × A.

A relation R in a set A is called , if (a, a) is an element of R, for every a is an element of A.

A relation R in a set A is called , if (a1, a2) is an element of R implies that (a2, a1) is an element of R, for all a1,a2 is an element of A.

A relation R in a set A is called , if (a1, a2) is an element of R and (a2, a3) is an element of R implies that (a1, a3)is an element of R, for all a1, a2,a3 is an element of A.

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

A function f : X → Y is defined to be , if the images of distinct elements of X under f are distinct, i.e., for every x1, x2 is an element of X, f(x1) = f(x2) implies x1 =x2.

A function f : X → Y is said to be , if every element of Y is the image of some element of X under f, i.e., for every y is an element of Y, there exists an element x in X such that f(x) = y.

A binary operation * on the set X is called , if a * b = b * a,for every a, b is an element of X.

A function f : X → Y is if and only if f is one-one and onto.