Introduction to Sets

Question 1

Roster Notation

Answer 1

A : {0,1,2,3}

Question 2

Set

Answer 2

unordered collection of objects

Question 3

elements

Answer 3

objects in a set

Question 4

subset

Answer 4

when every element in a subset A is in B

Question 5

proper subset

Answer 5

A is a proper subset of B if A != B

Question 6

cardinality

Answer 6

number of elements in a set (distinct)

Question 7

empty set

Answer 7

set with no elements

Question 8

important sets

Answer 8

Z, Z^+, N, Q, R

Question 9

Z

Answer 9

set of integers

Question 10

N

Answer 10

set of non-negative numbers

Question 11

Q

Answer 11

set of rational numbers

Question 12

R

Answer 12

set of real numbers

Question 13

set builder notation of A = {1,3,5,7,9}

Answer 13

{x | x is an odd positive integer less than 10}

Question 14

universal set

Answer 14

set containing all elements mentioned in a particular context

Question 15

power set

Answer 15

given a set S, the power set is a set of all subsets

Question 16

cardinality of a power set

Answer 16

2^|s| = 2^n

Question 17

string

Answer 17

sequence of characters

Question 18

alphabet

Answer 18

set of characters used in a set of strings, for the set of strings

Question 19

length of string

Answer 19

the number of characters

Question 20

binary string

Answer 20

string whose alphabet is {0,1}

Question 21

bit

Answer 21

character in a binary string

Question 22

n-bit string

Answer 22

string of length n

Question 23

the set of binary strings of length n

Answer 23

{0,1}^n

Question 24

empty string

Answer 24

unique string whose length is 0 and is usually denoted by alpha

Question 25

{0,1}^0

Answer 25

{alpha}

Question 26

concatenation

Answer 26

of strings s and t (st) is a longer string obtained by putting s and t together

Question 27

disjoint

Answer 27

if intersection of two sets is empty (empty set)

Question 28

pairwise disjoint

Answer 28

a sequence of sets A1,A2, A3…. An, if every pair of distinct sets in the sequence is disjoint

Question 29

partition of non-empty set

Answer 29

a collection of non-empty subsets of A such that each element of A is in exactly one of the subsets