Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)​

Sagot :

LammettHash

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.