Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. since {1, 2, . . . , 6} is the set of all possible

Since {1, 2, . . . , 6} is the set of all possible outcomes...

50.1K

Verified Solution

Question

Advance Math

Since {1, 2, . . . , 6} is the set of all possible outcomes of athrow with a regular die, the set of all possible outcomes of athrow with two dice is Throws := {1, 2, . . . , 6} × {1, 2, . . . ,6}. We define eleven subsets P2, P3, . . . , P12 of Throws asfollows: Pk := {: m + n = k} for k ∈ {2, 3, . . . ,12}. For example, P3 is the set of all outcomes for which the sumof the two numbers of dots thrown is 3.

(a) Show that the sets P2, P3, . . . , P12 form a partition ofthe set Throws.

(b) Let R be the equivalence relation on Throws that has P2, P3,. . . , P12 as its equivalence classes. Give a definition of R bymeans of a description.

(c) Give a complete system of representatives for theequivalence relation R.

Answer & Explanation Solved by verified expert
4.1 Ratings (517 Votes)
GivenLet S be the set of all possible outcomes of twodicesthereforeS 11 12 13 14 15 16 21 22 23 24 25 2631 32 33 34 35 3641 42 43 44 45 4651 52 53 54 55 5661 62 63 64 65 66According to QuestionPk m n kP2 11P3 12 21P4 13 31 22P5 14 41 23    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

0 a dominant gene with Huntington s disease a degenerative brain disorder caused by Mark...

Biology
Q

A solid sphere made of insulating material has a radius R and has a total...

Physics
Q

Two electric bulbs whose resistances are in the ratio of 1 2 are connected in...

Physics
Q

Find the maximum value of f x y z 30x 3y 21z on the sphere...

Geometry
Q

Let 9 A 2 25 4 Find an invertible matrix C and a diagonal matrix...

Basic Math
Q

For the ellipse x 132 y 7 1 the eccentricity is e

Calculus
Q

Find the formula for an exponential function that passes through the two points given x...

Algebra
Q

Exercise 6-3(Algo) Reconciliation of Absorption and Variable Costing Net Operating Incomes [LO6-3] [The...

Accounting
Q

When the level of activity increases, variable costs will: O A. increase per unit. OB....

Accounting
Q

A company has the following purchases and sales during March. Using the FIFO perpetual inventory...

Accounting
Q

Groro Company bills a client $64,000 for services provided and agrees to accept the following...

Accounting
Q

Examples of plant assets are: (Select all that apply.) Multiple select question. ...

Accounting