Check the working ( set )

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In summary, using algebraic laws of sets, it was shown that for any set A and set B, the intersection of the union of A and B with the union of A and the complement of B is equal to A. This was proven through the following steps: first, the intersection was expanded to include the union of B and A and the intersection of B and the complement of B. Then, using the distributive property, the union of A and B was intersected with A. Finally, through further expansion and simplification, it was shown that the result is equivalent to A.
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using algebraic laws of sets, show that, for any set A and set B that

( A U B ) [inter] ( A U B' ) = A


this is my working

( A U B ) [inter] ( A U B' )

= A U ( B [inter] A ) U ( B [inter] B' )

= ( A U B ) [inter] ( A U A )

= ( A U B ) [inter] A

= A U ( B [inter] A )

= A ( shown )


i think this working is wrong. is there other way better than this?
 
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  • #2
denian,
I think the 1st step should be

( A U B ) [inter] ( A U B' )

= A[inter]A U A[inter]B' U B[inter]A U B[inter]B'
 
  • #3
ok. i don't even know we can expand it that way.
thank you.
 

What is "Check the working (set)" and why is it important?

"Check the working (set)" is a phrase commonly used in scientific research to refer to the process of verifying that a particular procedure or experiment is functioning correctly and producing accurate results. It is important because it ensures the reliability and validity of the data being collected, which is essential in drawing accurate conclusions and making scientific advancements.

How do you check the working (set) of a scientific experiment or procedure?

The method for checking the working (set) of a scientific experiment or procedure may vary depending on the specific experiment or procedure being performed. However, some common steps include making sure all equipment is calibrated and functioning properly, following the correct protocols and procedures, and conducting control experiments to compare results. It is also important to document and track any changes or adjustments made during the experiment.

What are some common errors that can occur during the "check the working (set)" process?

Some common errors that can occur during the "check the working (set)" process include equipment malfunctions, human error, and environmental factors. It is important to be aware of these potential errors and take steps to minimize their impact on the experiment or procedure.

How can you ensure the accuracy and reliability of the "check the working (set)" process?

To ensure the accuracy and reliability of the "check the working (set)" process, it is important to follow established protocols and procedures, use properly calibrated equipment, and conduct multiple tests or control experiments. It is also helpful to have multiple researchers independently verify the results and findings.

What should you do if the "check the working (set)" process reveals errors or inconsistencies in the data?

If the "check the working (set)" process reveals errors or inconsistencies in the data, it is important to document the issue and investigate the source of the problem. This may involve repeating the experiment, troubleshooting equipment, or adjusting procedures. It is crucial to address any issues before drawing conclusions or making decisions based on the data.

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