I need help concerning venn diagrams shading

[chijioke]

Please I am trying to show these things:
[math]1. ~~ A^{\prime}[/math][math]2.~~B^{\prime}[/math][math]3.~~A^{\prime} \sqcup B^{\prime}[/math][math]4.~~A^{\prime} \sqcap B^{\prime}[/math] For #1 this is what I showed

For #2 I showed

For #3, I combined 1 and 2 as in

Then finally for #4, I combined 3 and 4 as in
Am I correct?

 

[blamocur]

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.

As for #4, do colors matter? I.e. does your answer contain both blue and red areas?

 

[Dr.Peterson]

Please I am trying to show these things:
[math]1. ~~ A^{\prime}[/math][math]2.~~B^{\prime}[/math][math]3.~~A^{\prime} \sqcup B^{\prime}[/math][math]4.~~A^{\prime} \sqcap B^{\prime}[/math] 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?

Consider elements 1, 2, 3, 4 as shown here:

​

Which are in [imath]A'[/imath]? Which are in [imath]B'[/imath]? Which are in [imath]A'\cup B'[/imath]? Which are in [imath]A'\cap B'[/imath]?

 

[pka]

For 3 & 4 you should use
[imath]\begin{gathered} \# 3\quad (A \cup B)' = A' \cap B' \\ \# 4\quad (A \cap B)' = A' \cup B' \\ \end{gathered}[/imath]

 

[Dr.Peterson]

For 3 & 4 you should use
[imath]\begin{gathered} \# 3\quad (A \cup B)' = A' \cap B' \\ \# 4\quad (A \cap B)' = A' \cup B' \\ \end{gathered}[/imath]

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.

[math]1. ~~ A^{\prime}[/math][math]2.~~B^{\prime}[/math][math]3.~~A^{\prime} \sqcup B^{\prime}[/math][math]4.~~A^{\prime} \sqcap B^{\prime}[/math]

I forgot to ask whether you intentionally used the "square cup" ([imath]\sqcup[/imath]) and "square cap" ([imath]\sqcap[/imath]) symbols instead of the proper "cup" ([imath]\cup[/imath]) and "cap" ([imath]\cap[/imath]) 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.

 

[chijioke]

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.

As for #4, do colors matter? I.e. does your answer contain both blue and red areas?

No, colour does not matter. I am just trying to show to the intersection.

 

[pka]

View attachment 36534

No, colour does not matter. I am just trying to show to the intersection.
View attachment 36537

The set notation [imath]x\in(A'\cup B')[/imath] is read [imath]x\text{ not in }A\text{ or not in }B[/imath].​

The set notation [imath]x\in(A'\cap B')[/imath] is read [imath]x\text{ not in }A\text{ and not in }B[/imath].​

Therefore, in the diagram above the red area is [imath](A'\cap B')[/imath]. i,e, Remove the purple area.​

[imath][/imath][imath][/imath][imath][/imath]

 

[Dr.Peterson]

View attachment 36534

No, colour does not matter. I am just trying to show to the intersection.
View attachment 36537

Your first picture shows [imath]A\cup B[/imath], not [imath]A'\cup B'[/imath]:

​

Your second picture shows [imath]A\cap B[/imath], not [imath]A'\cap B'[/imath]:

​

Please try doing one of the things that have been suggested, rather than making guesses.

 

[chijioke]

I forgot to ask whether you intentionally used the "square cup" ([imath]\sqcup[/imath]) and "square cap" ([imath]\sqcap[/imath]) symbols instead of the proper "cup" ([imath]\cup[/imath]) and "cap" ([imath]\cap[/imath]) 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 intend using [math]\cup[/math] and [math]\cap[/math] and not [math]\sqcap[/math] and [math]\sqcup[/math]

 

[chijioke]

Consider elements 1, 2, 3, 4 as shown here:

​

Which are in [imath]A'[/imath]? Which are in [imath]B'[/imath]? Which are in [imath]A'\cup B'[/imath]? Which are in [imath]A'\cap B'[/imath]?

I relabelled the diagram in order to show set A and B.
[imath]A'=\{3,4\}[/imath]
[imath]B'=\{1,4\}[/imath]
[imath]A'\cup B'=\{1,3,4\}[/imath]
[imath]A'\cap B'=\{4\}[/imath]
From what you ask me to show above, I can now see that [imath]A'\cup B'=\{1,3,4\}[/imath] is and that
[imath]A'\cap B'=\{4\}[/imath] is

 

[chijioke]

And that [imath]A'\cap B'=\{4\}[/imath] is

 

[blamocur]

I can now see that A′∪B′={1,3,4}A'\cup B'=\{1,3,4\}A′∪B′={1,3,4} is

I agree with you formula ({1,3,4}), but the picture does not look right.

 

[chijioke]

I agree with you formula ({1,3,4}), but the picture does not look right.

What made picture not look right ? Is it because I did not draw it digitally?

 

[blamocur]

What made picture not look right ? Is it because I did not draw it digitally?

I don't see a diagram with {1,3,4} shaded.

 

[Dr.Peterson]

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:

I relabelled the diagram in order to show set A and B.View attachment 36566
[imath]A'=\{3,4\}[/imath]
[imath]B'=\{1,4\}[/imath]
[imath]A'\cup B'=\{1,3,4\}[/imath]
[imath]A'\cap B'=\{4\}[/imath]
From what you ask me to show above, I can now see that [imath]A'\cup B'=\{1,3,4\}[/imath] isView attachment 36569

 

[chijioke]

[imath]A'\cup B'=\{1,3,4\}[/imath] is
I think it is correct now.

 

[Dr.Peterson]

[imath]A'\cup B'=\{1,3,4\}[/imath] isView attachment 36605
I think it is correct now.

Yes, it is. Note that this demonstrates, as you were told in post #4, that [imath](A \cap B)' = A' \cup B'[/imath]. The unshaded region is the intersection.