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Is empty set part of every set?by sozener1
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#1
Mar3014, 06:23 PM

P: 16

you have a power set of s
represented by p(s) and s is { x is integer and either x=<2 or x>=5} and you have another set d = {{3 2 1}, {4}, {6, 7}, {5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I meant to include { } the empty set as well since it is a subset of everyset??? 


#2
Mar3014, 06:49 PM

P: 991

In the question above, how many elements are in set d? Of those elements, which are members of p(s)? 


#3
Mar3014, 06:53 PM

P: 85

Hope that answers your question. 


#4
Mar3114, 01:23 AM

P: 1,304

Is empty set part of every set?
The empty set is an actual element of the power set.
The empty set is also a subset of the power set. The empty set is not an actual element of d. The empty set is a subset of d. The intersection considers elements of both sets, so the empty set is not an element of the intersection. But, the empty set is a subset of the intersection. The fact that the empty set is an element of the power set means that in addition to the empty set being a subset of the power set, the "set of the empty set" is also a subset of the power set, but this is not true for d. This is the difference. 


#5
Mar3114, 10:12 AM

Sci Advisor
P: 3,313

When speaking about sets, it's tempting to use phrases that don't have precise definitions like "is a part of" and "is contained in" or "contains". This question is a good example of why the more specific phrases "is a subset of" and "is an element of" are needed.



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