Purchase Solution

Proof about union and cardinalities

Not what you're looking for?

Ask Custom Question

Please help with the following problem. Provide a step by step explanation.

Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the sets:

#(A_1 union A_2 union...union A_n) = #A_1 + #A_2 +...+ # A_n

* Use that fact that the statement is true for n=2

Purchase this Solution
Solution Summary

This solution helps put together a proof about union and cardinalities. It helps prove that finite sets are pairwise-dispoint and that an intersection is a finite set. Step by step calculations are given.

Solution Preview

Problem: Show that given finite sets A_1, A_2,...,A_n, that are pairwise-disjoint, that is A_i intersection A_ j = empty set for all i not equal to j, then their union is a finite set and the cardinality of their union is the sum of the cardinalities of the sets: #(A_1 union A_2 union...union A_n) = #A_1 + #A_2 +...+ # A_n. Use that fact that the ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Providing proof about Cardinality

    (ii) To prove the second equality, let us consider any finite sets A, B, C with cardinalities a, b, c resp., and show that the sets A^BxA^C and A^(B+C) are bijective. Here B+C denotes the disjoint union of B and C.

  • Examining Proof about Cardinality

    But, as we already have proved, AxB and BxA are bijective, and hence have the same cardinalities. Therefore, nxm=mxn. The proof about cardinality is examined in the following posting.

  • Set Sizes

    517206 Set Sizes Find the number of elements in A_1 [the union of] A_2 [the union of] A_3 if there are 100 elements in A_1, 1000 in A_2, and 10,000 in A_3 if: a) A_1 [is a subset of] A_s and A_2 [is a subset of] A_3.

  • Proof about Set Theory

    454714 Proof about Set Theory Let A, B, C be sets and let X be a set containing A, B, C as subsets.

  • Joe, the owner of the ice-cream shop, purchases ice cream fr

    Draw an REA diagram, complete with cardinalities, for Joe's expenditure cycle REA diagram with cardinalities Joe, the owner of the ice-cream shop, purchases ice cream from two vendors.

  • The common notion 5 "The whole is greater than the part"

    But the cardinality of E and O is the same as the cardinality of N. The cardinalities of infinite sets are called transfinite numbers.

  • Object Oriented Software Design

    The minimum and maximum cardinalities of each relationship is given.

  • REA diagram with cardinalities, for Joe's revenue cycle

    Draw an REA diagram, complete with cardinalities, for Joe's revenue cycle.

  • ERD using MySQL modeling tool

    The diagram must include all entities, attributes, and relationships. Primary keys and foreign keys must be clearly identified on the diagram. Write all appropriate connectivities and cardinalities on the ERD. a).

View More Related Solutions