Question

A = Set of Face Cards

Answer 1

The probability based on the information given is illustrated below.

How to compute the values?

a. cardinality of set D

cardinality is simply the number of elements in the set

Set D = {red colored cards} = 26 elements

Cardinality = 26

b. power set of H

the set of all subsets of the Set including the Set itself and the null or empty set.

Set H = 3 face cards (hearts) = 3 elements

No. of subsets =  = 8

Power set of H = 8

c. are set L and N are disjoint or overlapping

L = {H2,H4,H6,H8,H10}

N = {D3,D5,D7,D9}

Both are disjoint

d. are sets J and K are equal sets or equivalent sets?

Equal sets are defined as the sets that have the same cardinality and all equal elements.

Two sets are said to be equivalent if they have the same cardinality

J = {D queen, D king , D joker}

K = { C queen, C king , C joker}

Both the sets are equivalent sets.

e. are set D and F overlapping if so find the card that are common

D= { red couloured cards}

F = { set of even cards}

yes , they are overlapping

common cards are red coloured even cards

= { H2,H4,H6,H8,H10,D2,D4,D6,D8,D10}

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Complete question:

Take a deck of playing cards. Form following sets out of those:

A =Set of Face Cards

B = Set of Red Coloured Face Cards

C = Set of Black Coloured Face Cards D = Set of Red Coloured Number Cards E = Set of Black Coloured Number Cards

F = Set of Even Number Cards

G = Set of Odd Number Cards

H = Set of Face Cards (Hearts)

I = Set of Face Cards (Spades)

J = Set of Face Cards (Diamonds)

K = Set of Face Cards (Clubs)

L = Set of Even Numbered Cards (Hearts) M = Set of Even Cards (Spades) N = Set of Odd Cards (Diamonds)

O = Set of Odd Cards (Clubs)

find the Following:

a. cardinality of set D

b. power set of H

c. are set L and N are disjoint overlapping d. are sets J and K are equal sets or equivalent sets ? justify your answer

e. are set D and F overlapping if so find the card that are common