The function that uses the previous term to find the next term in the sequence is called a ______ function

• A) bijective
• B) none of these
• C) recursive
• D) onto

Which of the following sets is uncountable?

• A) Set of even integers
• B) Set of prime numbers
• C) Set of real numbers
• D) Set of odd integers

What is recursion in mathematics?

• A) None of these
• B) Solving equations using matrices
• C) Finding derivatives of functions
• D) A function that calls itself

The Cartesian product of two denumerable sets is:

• A) Always finite
• B) Sometimes denumerable
• C) Always denumerable
• D) Some times finite

The set of all possible ordered pairs of natural numbers is:

• A) Countable
• B) Uncountable
• C) non-denumerable
• D) Finite

Which set is NOT an example of a countable set?

• A) Set of natural numbers
• B) Set of integers
• C) Set of rational numbers
• D) Set of real numbers

In a recursive sequence, each term is defined as a function of ___________.

• A) None of these
• B) Only the preceding term
• C) Both the preceding term and the first term
• D) Only the first term

Countable sets include:

• A) Infinite set only
• B) Both finite and denumerable sets
• C) Denumerable sets only
• D) Finite sets only

Which of the following statements about countable sets is FALSE?

• A) Countable sets can be infinite.
• B) Every subset of a countable set is countable.
• C) Countable sets have a cardinality equal to that of the natural numbers.
• D) Countable sets are always finite.

Which of the following sets is countable?

• A) Set of complex numbers
• B) Set of real numbers
• C) Set of rational numbers
• D) Set of irrational numbers

Two sets A = {pencil, copy} and B = {history, maths}are ________ sets.

• A) infinite
• B) equipotent
• C) None of these
• D) equal

If one set in a Cartesian product is uncountable, then the Cartesian product is:

• A) Sometimes denumerable
• B) Always denumerable
• C) Always uncountable
• D) Sometimes uncountable

Which of the following statement holds for a set of rational numbers?

• A) It is uncountable.
• B) It is non-denumerable.
• C) It is denumerable.
• D) It does not contain any denumerable subset.

If a lower bound of A precdes every other lower bound of A, then it is called the infimum of A

• A) Given statement is true.
• B) Given statement is false.
• C)
• D)

Let A be an ordered set. Then A is said to be well-ordered if every subset of A contains a first element.

• A) Given statement is true.
• B) Given statement is false.
• C)
• D)

The ordinal number of the set P of counting numbers is denoted by ω.

• A) false
• B) true
• C)
• D)

Any well-ordered set A is not linearly ordered.

• A) Given statement is false.
• B) Given statement is true.
• C)
• D)

Let A be a well-ordered set. The initial segment s(a) of an element a ϵ A consists of all elements in A which strictly precedes a.

• A) Given statement is false.
• B) Given statement is true.
• C)
• D)

Let S be a partially ordered set, and let A be a subset of S. If A has an upper bound ,we say A is bounded above.

• A) Given statement is false.
• B) Given statement is true.
• C)
• D)

The ordinal number of set {a,{b,c}} is __________________.

• A) 3
• B) 0
• C) 2
• D) 1