Simplify expressions

[foukr]

Consider some universe (like N) and its subsets A, B.
Simplify the following expressions (and prove equality).



Can you explain to me how I can simplify the following expressions?
If you were so willing and wrote to me and explain to me a specific solution procedure, it would be very nice of you

 

[Deleted member 4993]

Consider some universe (like N) and its subsets A, B.
Simplify the following expressions (and prove equality).

View attachment 14254

Can you explain to me how I can simplify the following expressions?
If you were so willing and wrote to me and explain to me a specific solution procedure, it would be very nice of you

Please share your work/thoughts about this assignment.

Please follow the rules of posting in this forum, as enunciated at:

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[Steven G]

Consider some universe (like N) and its subsets A, B.
Simplify the following expressions (and prove equality).

View attachment 14254

Can you explain to me how I can simplify the following expressions?
If you were so willing and wrote to me and explain to me a specific solution procedure, it would be very nice of you

1st one. Draw a venn diagram--Two circles that overlap. But a box around the whole thing. Shade in (A and B) and then shade in (A and B'). Wherever you have shading will be your answer.
Alternatively you can think about what it is saying. When it comes to set A, part of A will be in set B and part of A will Not be in B (so it will be in B') What do you think the union of those two sets will be???


2nd problem: What do you think (B intersect the empty set) will equal? So what is A union that result?

4th problem: What take of things to you raise the number 2 to? (numbers, sets, elephants, physics,...). What are you raising 2 to?

 

[pka]

Consider some universe (like N) and its subsets A, B.
Simplify the following expressions (and prove equality).
View attachment 14254
Can you explain to me how I can simplify the following expressions?
If you were so willing and wrote to me and explain to me a specific solution procedure, it would be very nice of you

If \(\displaystyle \mathcal{U}\) is the universe then \(\displaystyle B\cup\overline{B}=\mathcal{U}\)
So
\(\displaystyle (A\cap B)\cup(A\cap\overline{B})\\=A\cap(B\cup\overline{B})\\=A\cap\mathcal{U}\\=A\)

 

[foukr]

Thank's you all for understanding. I am sorry for my English is not my strong side.

Can you look at my solution and tell me if it's correct?
Can you prove equality and Simplify [MATH] 2^{ A, B } [/MATH]

 

[pka]

Thank's you all for understanding. I am sorry for my English is not my strong side.
Can you look at my solution and tell me if it's correct?
Can you prove equality and Simplify [MATH] 2^{ A, B } [/MATH]

In every western country I know the notation \(\displaystyle 2^A\) is the set of all functions from set \(\displaystyle A\) to \(\displaystyle \{0,1\}\)
Or \(\displaystyle A^B\) is the set of all functions from \(\displaystyle A\to B\).
So I know of no meaning for \(\displaystyle 2^{A,B}\).
If you still want help you need to define all terms.