Consider any two finite sets A and B. Prove that |A×B|=|A||B|

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Colby Messinger answered 1 year ago

Let A and B be finite sets. Prove the following: (a) |A∪B|=|A|+|B|−|A∩B| (b) |A × B|...

Let A and B be finite sets. Prove the following: (a) |A∪B|=|A|+|B|−|A∩B| (b) |A × B| = |A||B| (c) |{f : A → B}| = |B||A|

Prove the following Theorems: 1. A finite union of compact sets is compact. 2. Any intersection...

Prove the following Theorems: 1. A finite union of compact sets is compact. 2. Any intersection of compact set is compact. 3. A closed subset of a compact set is compact. 4. Every finite set in IRn is compact.

1) a) Prove that the union of two countable sets is countable. b) Prove that the...

1) a) Prove that the union of two countable sets is countable. b) Prove that the union of a finite collection of countable sets is countable.

Prove the following using any method you like: Theorem. If A, B, C are sets, then...

Prove the following using any method you like: Theorem. If A, B, C are sets, then (A ∪ B) \ C = (A \ C) ∪ (B \C) and A ∪ (B \ C) = (A ∪ B) \ (C \ A)

Prove the following statements! 1. If A and B are sets then (a) |A ∪ B|...

Prove the following statements! 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b) injective but not surjective. (c) surjective but not injective. (d)...

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If...

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|. 2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|. 3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b)...

Averages and variation Consider two data sets A and B. The sets are identical except the...

Averages and variation Consider two data sets A and B. The sets are identical except the high value of the data set B is three times greater than the high value of data set A. (a) How does the median of the two data sets compare? (b) How do the means of the two data sets compare? (c) How do the standard deviations of the two data sets compare? (d) How do the box- and –whisker plots of the two...

Given two sets A,B prove A<---> B either using the definition of the schroeder-bernstein theorem

A student suggests that for any two sets A and B: Statement 1: AUB' = (B/A)'...

A student suggests that for any two sets A and B: Statement 1: AUB' = (B/A)' Statment 2: AUB' will never contain an element in set B Is each of these statements correct or incorrect? Use and example or visual representation in your explanation please.

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let...

Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. Let S = {0, 1, . . . , 23} and define f : Z→S by f(k) = r when 24|(k−r). If g : S→S is defined by (a) g(m) = f(7m) then g is injective and (b) g(m) = f(15m) then g is not injective. 2. Let f : A→B and g : B→C be injective. Then g ◦f : A→C is injective. 3....

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