Consider elements 1, 2, 3, 4 as shown here:Please I am trying to show these things:
1. A′2. B′3. A′⊔B′4. A′⊓B′ For #1 this is what I showed
View attachment 36513
For #2 I showed
View attachment 36514
For #3, I combined 1 and 2 as in
View attachment 36515
Then finally for #4, I combined 3 and 4 as inView attachment 36516
Am I correct?
Make that "could use". Quite likely, this exercise is intended to help students discover those facts (in addition to getting used to what union and intersection mean). It's good to initially learn to do exactly what an expression means, before learning shortcuts, as valuable as those are.For 3 & 4 you should use
#3(A∪B)′=A′∩B′#4(A∩B)′=A′∪B′
I forgot to ask whether you intentionally used the "square cup" (⊔) and "square cap" (⊓) symbols instead of the proper "cup" (∪) and "cap" (∩) for union and intersection. The symbols you used are special-purpose symbols used for certain variations on union and intersection in different contexts (I don't think I've ever had reason to use them), and are not likely what you really mean.1. A′2. B′3. A′⊔B′4. A′⊓B′
No, #3 is not correct. Try shading both A' and B' on the same diagram (with different colors for clarity), then let us know what do you think their union is.
No, colour does not matter. I am just trying to show to the intersection.As for #4, do colors matter? I.e. does your answer contain both blue and red areas?
View attachment 36534
No, colour does not matter. I am just trying to show to the intersection.
View attachment 36537
Your first picture shows A∪B, not A′∪B′:View attachment 36534
No, colour does not matter. I am just trying to show to the intersection.
View attachment 36537
I intend using ∪ and ∩ and not ⊓ and ⊔I forgot to ask whether you intentionally used the "square cup" (⊔) and "square cap" (⊓) symbols instead of the proper "cup" (∪) and "cap" (∩) for union and intersection. The symbols you used are special-purpose symbols used for certain variations on union and intersection in different contexts (I don't think I've ever had reason to use them), and are not likely what you really mean.
I relabelled the diagram in order to show set A and B.Consider elements 1, 2, 3, 4 as shown here:
Which are in A′? Which are in B′? Which are in A′∪B′? Which are in A′∩B′?
I agree with you formula ({1,3,4}), but the picture does not look right.I can now see that A′∪B′={1,3,4}A'\cup B'=\{1,3,4\}A′∪B′={1,3,4} is
What made picture not look right ? Is it because I did not draw it digitally?I agree with you formula ({1,3,4}), but the picture does not look right.
I don't see a diagram with {1,3,4} shaded.What made picture not look right ? Is it because I did not draw it digitally?
Just look at what you drew. You only shaded in 1 and 3, not 1, 3, 4:What made picture not look right ? Is it because I did not draw it digitally?
I relabelled the diagram in order to show set A and B.View attachment 36566
A′={3,4}
B′={1,4}
A′∪B′={1,3,4}
A′∩B′={4}
From what you ask me to show above, I can now see that A′∪B′={1,3,4} isView attachment 36569
Yes, it is. Note that this demonstrates, as you were told in post #4, that (A∩B)′=A′∪B′. The unshaded region is the intersection.