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Q: Is the null set an element of every set?

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Let set A = { 1, 2, 3 } Set A has 3 elements. The subsets of A are {null}, {1}, {2}, {3}, {1,2},{1,3},{1,2,3} This is true that the null set {} is a subset. But how many elements are in the null set? 0 elements. this is why the null set is not an element of any set, but a subset of any set. ====================================== Using the above example, the null set is not an element of the set {1,2,3}, true. {1} is a subset of the set {1,2,3} but it's not an element of the set {1,2,3}, either. Look at the distinction: 1 is an element of the set {1,2,3} but {1} (the set containing the number 1) is not an element of {1,2,3}. If we are just talking about sets of numbers, then another set will never be an element of the set. Numbers will be elements of the set. Other sets will not be elements of the set. Once we start talking about more abstract sets, like sets of sets, then a set can be an element of a set. Take for example the set consisting of the two sets {null} and {1,2}. The null set is an element of this set.

The definition of subset is ; Set A is a subset of set B if every member of A is a member of B. The null set is a subset of every set because every member of the null set is a member of every set. This is true because there are no members of the null set, so anything you say about them is vacuously true.

First of all, the null set( denoted by is a subset of every set. But it being a proper set or improper set is debatable. Many mathematicians regard it as an improper set, and rightly have as when we say a set is a subset of another, the super set always contains at least one element. For eg,. Let A be the set, in roster form we take it as: A = {ϕ}, we clearly see n(A)=1 then P(A) = {ϕ,{ϕ}} We observe that at least a set must have 1 element for it to have a proper set, but if we take A = ϕ ( i.e. n(A)=0), then clearly ϕ and A itself are improper sets of A and. Hence the minimum amount of proper sets a set has is nil and improper is 2. But I have seen a few high school text books who regard null set as a proper set, which is totally false, arguable by mathematicians, clearly signifying the lethargy of authors of the book failing to update their error driven books. I assure you, that null set is an improper set of every set.

A set with 12 elements has 212 = 4096 subsets, including the null set (no elements) and the original full set, which is not a proper subset of itself.Here's the logic behind it:In making up a subset, you have a two-way choice for each element: to include it or to exclude it.These choices are independent: whether or not you include, say, element #4 doesn't depend in any way on your choices for the other 11.So you havetwo choices for element #1 (in or out)Then you have two choices for element #2. Combined with the two for #1, that makes four: in-in {1,2}, in-out {1}, out-in {2}, out-out {} (the null set, Ø).And you have two choices for #3... which makes 8 possibilities...and so on...... till you have 2x2x2x2x2x2x2x2x2x2x2x2 = 212 = 4096 possible subsets.

If your 7 element set is {a, b, c, d, e, f, g}, you would list a 3 element subset by taking any 3 elements of the set eg., {a, d, g} or {b, c, f}, etc. To count all of the subsets, the formula is 7C3, where 7C3 is 7!/(3!*4!), or 35 different unique 3 element subsets of a 7 element set.

Related questions

Yes - because, if something is an object of the null set, then it is also an element of the other set. Since nothing is an element of the empty set, the above statement is trivially true.

The null set. Every set is a subset of itself and so the null set is a subset of the null set.

Yes the null set is a subset of every set.

yes

empty set or null set is a set with no element.

Let set A = { 1, 2, 3 } Set A has 3 elements. The subsets of A are {null}, {1}, {2}, {3}, {1,2},{1,3},{1,2,3} This is true that the null set {} is a subset. But how many elements are in the null set? 0 elements. this is why the null set is not an element of any set, but a subset of any set. ====================================== Using the above example, the null set is not an element of the set {1,2,3}, true. {1} is a subset of the set {1,2,3} but it's not an element of the set {1,2,3}, either. Look at the distinction: 1 is an element of the set {1,2,3} but {1} (the set containing the number 1) is not an element of {1,2,3}. If we are just talking about sets of numbers, then another set will never be an element of the set. Numbers will be elements of the set. Other sets will not be elements of the set. Once we start talking about more abstract sets, like sets of sets, then a set can be an element of a set. Take for example the set consisting of the two sets {null} and {1,2}. The null set is an element of this set.

A null set is a set with nothing in it. A set containing a null set is still containing a "null set". Therefore it is right to say that the null set is not the same as a set containing only the null set.

The definition of subset is ; Set A is a subset of set B if every member of A is a member of B. The null set is a subset of every set because every member of the null set is a member of every set. This is true because there are no members of the null set, so anything you say about them is vacuously true.

Set it to null

The null set. It is a subset of every set.

Yes.The set of {Aleph-null, Aleph-one, ...}, which is the set of the different infinities, has infinity as an element.Aleph-null is the countable infinity.

No. An empty set is a subset of every set but it is not an element of every set.

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