Question

Homework help Anyone?

Answer 1

@ganeshie8 kindly

Answer 2

which q ?

Answer 3

sorry 1 and 3 sorry

Answer 4

Available?

Answer 5

#1 should be easy if you are familiar with powerset

Answer 6

{a, b, c}

lets list all the subsets with 0/1/2/3 elements :

0 : {}
1 : {a}, {b}, {c}
2 : {a, b}, {b, c}, {c, a}
3 : {a, b, c}

Answer 7

count them for part b

Answer 8

can u help me with that

Answer 9

count them for b ? like add all the ones given above ?

Answer 10

there ?

Answer 11

powerset of set A is a collection of all the subsets of A.

cardinality of a finite set is the number of elements in a set

Answer 12

how many subsets are there for the set {a, b, c} ?

Answer 13

three

Answer 14

what are they ?

Answer 15

{a,b}, {b,c} and {c,a}

Answer 16

those are subsets with just two elements

Answer 17

what about the subsets with 1 element, 3 elements and 0 elements ?

Answer 18

0 : `{}`
1 : `{a}`, `{b}`, `{c}`
2 : `{a, b}`, `{b, c}`, `{c, a}`
3 : `{a, b, c}`

Answer 19

ok i get you.

Answer 20

number of subsets with 0 elements = 1
number of subsets with 1 elements = 3
number of subsets with 2 elements = 3
number of subsets with 3 elements = 1

Answer 21

total number of subsets = ?

Answer 22

8

Answer 23

yes so we say the cardinality of powerset of {a, b, c} is 8

Answer 24

it refers to the size of a set

Answer 25

and the powerset of {a, b, c} would be :

{ {}, {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c} }

Answer 26

possible subsets for {a,b,c,d} will be 10?

Answer 27

try again

Answer 28

list them by size

Answer 29

subsets with 0 elements : {}

Answer 30

subsets with 1 elements : {a}, {b}, {c}, {d}

Answer 31

etc..

Answer 32

ok just a min

Answer 33

11?

Answer 34

list them all

Answer 35

list all the subsets with 2 elements

Answer 36

{a,b} {b,c} {c,d} {d,a} {b,d} {a,d}

Answer 37

Right, next list down all the subsets with 3 elements?

Answer 38

{a,b,c} {b,c,d} {a,b,d} {a,c,d}

Answer 39

next list all the subsets with 4 elements

Answer 40

{a,b,c,d}

Answer 41

so total how many subsets you got ?

Answer 42

12

Answer 43

number of subsets with 0 elements : 1
number of subsets with 1 elements : 4
number of subsets with 2 elements : 6
number of subsets with 3 elements : 4
number of subsets with 4 elements : 1

Answer 44

add them again

Answer 45

sorry sorry

Answer 46

did not count some

Answer 47

cardinalty is the total number of subsets

Answer 48

cardinality of a set is the total number of elements in it

Answer 49

powerset is a collection of all the subsets

Answer 50

so for {a,b,c,d } cardinality is 4

Answer 51

Yep!

Answer 52

Thankya. For section (e) ?

Answer 53

do you see any pattern ?

Answer 54

i cant guess.

Answer 55

Available?

Answer 56

cardinality of powerset with 3 elements = 8 = 2^3
cardinality of powerset with 4 elements = 16 = 2^4
...
cardinality of powerset with n elements = 2^n ?

Answer 57

https://proofwiki.org/wiki/Cardinality_of_Power_Set

Answer 58

Thank you

Answer 59

Question 3 please.

Answer 60

hey il need to review my analysis notes a bit to answer that

Answer 61

maybe close this question and open a new question for #3, il try to answer if nobody does..

Answer 62

ok. Thank you.