[QUOTE=science_man_88;248380]{2},{3},{4},{2,3},{2,4},{3,4},{2,3,4},[/QUOTE]

You missed one. Hint: What is A intersect {5, 6, 7, 8}? Is this intersection not [i]by definition[/i] a subset of A? Isn't it also a subset of B?

[QUOTE]and there reversals as well as {3,2,4},{3,4,2},and {4,2,3} ? I'm guessing all of the largest ones could be considered equal and they could \therefore all be a version of the intersection[/QUOTE]

Not 'considered' equal. They [i]are[/i] equal.

Exercise:

1. Without referring to an example, explain what it means for one set to be equal to another.
2. Again, without referring to an example, explain what it means for one -tuple to be equal to another.

Hint your answer to the two questions should not be the same.

[QUOTE=Mr. P-1;248407]You missed one. Hint: What is A intersect {5, 6, 7, 8}? Is this intersection not [i]by definition[/i] a subset of A? Isn't it also a subset of B?



Not 'considered' equal. They [i]are[/i] equal.

Exercise:

1. Without referring to an example, explain what it means for one set to be equal to another.
2. Again, without referring to an example, explain what it means for one -tuple to be equal to another.

Hint your answer to the two questions should not be the same.[/QUOTE]

1) when 2 sets are equal they contain the same amount of elements with the same values but not necessarily the same order.

2) when n-tuples are equal they have the same amount of entries in the same order with the same values.


you seem to be pointing to the one I forgot the empty set ?

[QUOTE=science_man_88;248409]1) when 2 sets are equal they contain the same amount of elements with the same values but not necessarily the same order.

2) when n-tuples are equal they have the same amount of entries in the same order with the same values.


you seem to be pointing to the one I forgot the empty set ?[/QUOTE]

Good. To continue: how many elements in the intersection of
two sets A and B? In the union of A and B? In the empty set?

[QUOTE=science_man_88;248409]1) when 2 sets are equal they contain the same amount of elements with the same values but not necessarily the same order.[/QUOTE]

Is {1, 2, 3, 4} equal to {1, 2, 3, 4, 1}?

[QUOTE]you seem to be pointing to the one I forgot the empty set ?[/QUOTE]

Yes. The empty set is a subset of every set.

[QUOTE=davar55;248411]Good. To continue: how many elements in the intersection of
two sets A and B? In the union of A and B? In the empty set?[/QUOTE]

3. I'm not sure if it's 8 or 5 but I'd guess 8. 0 ?

[QUOTE=Mr. P-1;248414]Yes. The empty set is a subset of every set.[/QUOTE]

Does the empty set have any subsets?

[QUOTE=Mr. P-1;248414]Is {1, 2, 3, 4} equal to {1, 2, 3, 4, 1}?

[COLOR="Red"]my first guess is no, just on the basis that there's an extra 1 , which breaks my understanding as it violates the same number of elements. [/COLOR]

Yes. The empty set is a subset of every set.[/QUOTE]

I have to write something here the way I'm responding because it doesn't like an empty non quote area.

[QUOTE=science_man_88;248415]3. I'm not sure if it's 8 or 5 but I'd guess 8. 0 ?[/QUOTE]

Sorry, it's five. How many elements does this set have: {1, 2, 3, 4, 1}?

[QUOTE=Mr. P-1;248417]Does the empty set have any subsets?[/QUOTE]

well if every set has to have the empty set as a subset than doesn't that also apply to the empty set itself ? I would have to say yes on that basis.

[QUOTE=Mr. P-1;248421]Sorry, it's five. How many elements does this set have: {1, 2, 3, 4, 1}?[/QUOTE]

5.

[QUOTE=science_man_88;248415]3. I'm not sure if it's 8 or 5 but I'd guess 8. 0 ?[/QUOTE]

OK.

A has 4 elements, written |A| = 4.
B has 4 elements, written |B| = 4.

A intersect B has 3 elements. Correct.
A union B has 5 elements. Correct.
(Not 8 as you now see.)

The empty set has 0 elements. Correct.

The empty set is a subset of any other set.

Also, the empty set is a subset of itself.