Question

If a finite set A has n elements then n can be * A) any real number B) any natural number C) any integer D) any whole number

Answer 1

Answer:

Finite sets are sets that have a finite number of members. If the elements of a finite set are listed one after another, the process will eventually “run out” of elements to list.

Example:

A = {0, 2, 4, 6, 8, …, 100}

C = {x : x is an integer, 1 < x < 10}

An infinite set is a set which is not finite. It is not possible to explicitly list out all the elements of an infinite set.

Example:

T = {x : x is a triangle}

N is the set of natural numbers

A is the set of fractions

The number of elements in a finite set A is denoted by

n(A)

Example:

If A is the set of positive integers less than 12 then

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and n(A) = 11

If C is the set of numbers which are also multiples of 3 then

C = {3, 6, 9, …} and C is an infinite set

If D is the set of integers x defined by –3 < x < 6 then

D = {–2, –1, 0, 1, 2, 3, 4, 5} and n(D) = 8

If Q is the set of letters in the word ‘HELLO’ then

Q = {H, E, L, O} , n(Q) = 4 ← ‘L’ is not repeated.