This doesn't makes sense

If x e (A1 n A2 n 143 n ... ) then x is not the element of at least one of the sets.

This implies if x doesnt belong to intersection of 3 sets that means it doesn't blong to any set.

De Morgan's Law

I think this is false when C⊂B with elements of A U B

If A A B = A A C, then B

similar to

Symmetric difference with 3 sets

In Symmetric difference why is intersection of 3 not included, also what its associative.

Symmetric difference means "unique to" ? So AΔBΔC != (AΔB)ΔC

Cardinal Number of set Union of 4 Sets

I thinkg it should be - n(AUBUCUD)

= [Sum of number of elements in sets A, B, C and D]

- [Sum of number of elements of intersection of sets taken 2 at a time]

- [Sum of no. of elements of intersection of sets taken 3 at a time]

- Elements of intersection of all sets

Edited 17 hours ago17 hr by HbWhi5F

5 minutes ago, HbWhi5F said:

This doesn't makes sense

If x e (A1 n A2 n 143 n ... ) then x is not the element of at least one of the sets.

This implies if x doesnt belong to intersection of 3 sets that means it doesn't blong to any set.

De Morgan's Law

I think this is false when C⊂B with elements of A U B

If A A B = A A C, then B

similar to

Symmetric difference with 3 sets

In Symmetric difference why is intersection of 3 not included, also what its associative.

Symmetric difference means "unique to" ? So AΔBΔC != (AΔB)ΔC

Cardinal Number of set Union of 4 Sets

What is your question?

@Genady I am having problem understanding these

1 minute ago, HbWhi5F said:

@Genady I am having problem understanding these

What specifically don't you understand?

The OP is too noisy. I am having problem understanding it.

@Genady Explain this doesn't makes sense to me. This implies if x doesnt belong to intersection of 3 sets that means it doesn't blong to any set.

14 minutes ago, HbWhi5F said:

@Genady Explain this doesn't makes sense to me. This implies if x doesnt belong to intersection of 3 sets that means it doesn't blong to any set.

No, it does not imply that x doesn't belong to any set.

It implies that there is at least one set such that x doesn't belong to it.

IOW,

it does not imply that [math]x \notin A_1 \wedge x \notin A_2 \wedge x \notin A_3[/math].

It implies that [math]x \notin A_1 \vee x \notin A_2 \vee x \notin A_3[/math].

Yet IOW,

it does not imply that [math]\forall i , x \notin A_i[/math].

It implies that [math]\exists i , x \notin A_i[/math].

Edited 4 hours ago4 hr by Genady

Consider an example. Let set W be all women and set B be all black persons. The intersection of W and B contains all black women. If a person x doesn't belong to this intersection, then x is not a black woman. x can be a black person but not a woman, a woman but not a black person, or neither a black person nor a woman.

@Genady De Morgan's Law I think this is false when C⊂B with elements of A U B

2 minutes ago, HbWhi5F said:

@Genady De Morgan's Law I think this is false when C⊂B with elements of A U B

I don't know what that triangle sign means. Some set operation, I guess, but which? Union, intersection, subtraction...?

Edited 1 hour ago1 hr by Genady

@Genady https://www.geeksforgeeks.org/maths/symmetric-difference-of-sets/

51 minutes ago, HbWhi5F said:

@Genady https://www.geeksforgeeks.org/maths/symmetric-difference-of-sets/

How to Find the Symmetric Difference?

To find Symmetric difference between the two sets A and B, follow these steps:

1. Find elements that are unique to set A, which is A - B.

2. Find elements that are unique to set B, which is B - A.

3. Take Union of these unique elements: A Δ B = (A - B) ∪ (B -A)

This is a very roundabout way to say

Creat a set that only contains those elements that are in both A and in B. - Which has another name.

create a set which is the union of the set of all those elements that are in A but not in B with the set of all those elements which are in B but not in A.

I note you website uses both the term elements and members.

Have you lost interest in your previous set theory thread or were you just not going to answer me ?