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 February 5th, 2014, 04:55 AM #1 Newbie   Joined: Feb 2014 Posts: 21 Thanks: 0 Which statements are true? Hi, I'm a nontraditional (old fart ) student taking classes online. It has its advantages and disadvantages. One disadvantage is the time delay in getting your questions answered. I'm hoping this forum will be a supplement to my learning. I think I understand it but I'd feel much better someone would look over my shoulder... Now to the question: Which are true statements? Ø ? Ø states that an empty set is a proper set of an empty set. This is False because a subset can't be equal to a superset. Ø ? {x,y} states that an empty set is a proper set of set {x,y}. This is False because an empty set is not found in the finite set {x,y}. 0 ? Ø states that an zero is an element of an empty set. This is False because zero is a real number and can't be found in an empty set. Ø ? {Ø} states that an empty set is an element of the set "the empty itself". This is True because "the empty itself" contains an empty set. Am I on the right path?
 February 5th, 2014, 05:47 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Which statements are true? I think you're on the right track but your explanations are not precise. You also should clarify whether you are looking at subsets here or strictly proper subsets. Normally: $A \subset B$ Means A is a subset of B and is not equal to B; whereas: $A \subseteq B$ Means A is a subset of B and could be equal to B. Is this the terminology you are using? Also, note that: $\emptyset \subseteq B$ For every set B, including where B itself is the empty set.
 February 5th, 2014, 05:51 AM #3 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Which statements are true? Ø ? Ø states that an empty set is a proper set of an empty set. This is False because a subset can't be equal to a superset. This is false, as a set cannot be strictly a subset of itself. Although, it may be true depending on what you mean by ? Ø ? {x,y} states that an empty set is a proper set of set {x,y}. This is False because an empty set is not found in the finite set {x,y}. This is true. 0 ? Ø states that an zero is an element of an empty set. This is False because zero is a real number and can't be found in an empty set. Yes. Ø ? {Ø} states that an empty set is an element of the set "the empty itself". This is True because "the empty itself" contains an empty set. Yes, this one is tricky. I'd say {Ø} is "the set containing the empty set as an element".
 February 5th, 2014, 05:54 AM #4 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Which statements are true? 0 ? Ø states that an zero is an element of an empty set. This is False because zero is a real number and can't be found in an empty set. Note that there is only one empty set! So, you always say the empty set. Try to prove this.
 February 5th, 2014, 09:05 AM #5 Newbie   Joined: Feb 2014 Posts: 21 Thanks: 0 Re: Which statements are true? Thanks Pero, That's a big help! Joe
 February 5th, 2014, 10:01 AM #6 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Which statements are true? Can you prove there is only one empty set?
February 5th, 2014, 12:17 PM   #7
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Re: Which statements are true?

Quote:
 Originally Posted by Pero 0 ? Ø states that an zero is an element of an empty set. This is False because zero is a real number and can't be found in an empty set. Note that there is only one empty set! So, you always say the empty set. Try to prove this.
Hmm,

0 in the equation is an element
? means "is an element of"
Ø means "the set with no elements"

Not sure I know how to "prove" there is only one empty set.

 February 5th, 2014, 01:10 PM #8 Newbie   Joined: Feb 2014 Posts: 21 Thanks: 0 Re: Which statements are true? I'm just now learning this, but I'm reading further... could I prove it with a membership table? Note: I've not heard of a membership table until now. This is new to me.
 February 5th, 2014, 02:20 PM #9 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Which statements are true? If there were two empty sets, then in what way could they be different?

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