MTH100 Final Term Short Notes by VU Topper RM

Q1. (Marks:2-5) Vu-Topper RM Define a set?

A set is an unordered collection of distinct objects. Objects in the collection are called elements of the set.

Q2. (Marks:2-5) Vu-Topper RM What is roster method of sets?

The roster method of specifying a set consists of surrounding the collection of elements with braces. For example, the set of counting numbers from 1 to 5 would be written as {1, 2, 3, 4, 5}.

Q3. (Marks:2-5) Vu-Topper RM Define null set?

The set with no elements is called the empty set or the null set.

Q4. (Marks:2-5) Vu-Topper RM Define universal set?

The universal set is the set of all things pertinent to a given discussion and is designated by the symbol U

Q5. (Marks:2-5) Vu-Topper RM Define subset?

The set A is a subset of the set B, denoted A B, if every element of A is an element of B.

Q6. (Marks:2-5) Vu-Topper RM Define equal set?

Two sets A and B are equal if A B and B A. If two sets A and B are equal, we write A = B to designate that relationship.

Q7. (Marks:2-5) Vu-Topper RM Define intersection of sets?

The intersection of two sets A and B is the set containing those elements which are elements of A and elements of B. We write A B to denote an Intersection B. Example: If A = {3, 4, 6, 8} and B = {1, 2, 3, 5, 6} then A B = {3, 6}

Q8. (Marks:2-5) Vu-Topper RM Define union of sets?

The union of two sets A and B is the set containing those elements which are elements of A or elements of B. We write A B to denote A Union B. Example: If A = {3, 4, 6} and B = { 1, 2, 3, 5, 6} then A B = {1, 2, 3, 4, 5, 6}.

Q9. (Marks:2-5) Vu-Topper RM What are algebraic properties of sets? Or difference between commutative associative and distributive law?

Commutative:

Union and intersection are commutative operations. In other words, A B = B A and A ∩ B = B ∩ A

Associative:

Union and intersection are associative operations. In other words, (A B) C = A (B C) and (A ∩ B) ∩ C = B ∩ (A ∩ C)

Distributive:

Union and Intersection are distributive with respect to each other. In other words, A ∩ ( B C )= (A ∩ B) (A ∩ C) and A ( B ∩ C )= (A B) ∩ (A C)

Q10. (Marks:2-5) Vu-Topper RM Define cardinality? With two types?

Cardinality refers to the number of elements in a set A finite set has a countable number of elements An infinite set has at least as many elements as the set of natural numbers

Q11. (Marks:2-5) Vu-Topper RM Define complex number?

Numbers of the form a + bi are called complex numbers. a is the real part and b is the imaginary part. The set of complex numbers is denoted by C

Q12. (Marks:2-5) Vu-Topper RM Define absolute value?

The absolute value or modulus of a complex number is the distance the complex number is from the origin on the complex plane.

Q13. (Marks:2-5) Vu-Topper RM Define relation?

A mapping between two sets A and B is simply a rule for relating elements of one set to the other. A mapping is also called a relation.

Q14. (Marks:2-5) Vu-Topper RM Define domain and range?

The set consisting of members of the pre-image or inputs of a function is called its domain. For a given domain the set of possible outcomes or images of a function is called its range.