Is the Power Set of Cartesian Products Correct?

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Homework Help Overview

The discussion revolves around the concepts of power sets and Cartesian products, specifically focusing on the sets A, B, and C defined in the problem statement. Participants are exploring the calculations related to P(A*B) and |P(B*C)|.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the power set of the Cartesian product A*B and the size of the power set of B*C. Some participants question the notation used for the Cartesian product and seek clarification on its definition.

Discussion Status

Participants are actively clarifying the notation and definitions related to Cartesian products. One participant confirms the original poster's calculations, while others provide insights into the meaning of the absolute value signs in the context of set size.

Contextual Notes

There is some uncertainty regarding the notation for Cartesian products, with participants discussing the appropriate symbols to use. The original poster's understanding of the problem is still developing, as they seek confirmation of their answers.

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Homework Statement



if A ={a}, B={b,c}, C={d,e,f,g,h,i,j}

Find P(A*B)
and |P(B*C)|



Homework Equations





The Attempt at a Solution



so for the first one I had

[{(a,b)}, {(a,c)}, {(a,b),(a,c)}, ∅]

and secondly 2^14.

is this right I don't know what is meant by the use of this |..| around a power set?
 
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What does A*B mean?
 
LCKurtz said:
What does A*B mean?

Sorry its meant to mean A times B

dont know what the proper sign is ? or do I just use ()
 
charmedbeauty said:
Sorry its meant to mean A times B

dont know what the proper sign is ? or do I just use ()

Sets have union and intersection operations. What is the definition of A "times" B?
 
LCKurtz said:
Sets have union and intersection operations. What is the definition of A "times" B?

Its a Cartesian product
 
Ok, now that I understand your notation your answers look fine. The absolute value signs around a set just means how many elements it contains. So your ##2^{14}## is correct.
 

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