neve domain was triggered too early. This is usually an indicator for some code in the plugin or theme running too early. Translations should be loaded at the init action or later. Please see Debugging in WordPress for more information. (This message was added in version 6.7.0.) in /home/mathze5/public_html/learnermath.com/wp-includes/functions.php on line 6114This page will look to introduce the concept of Math sets and subsets, and the notation that is involved.<\/p>\n
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In Math, a set is a collection of objects or elements.\n There is also the case where a set can have no elements at all in it.\n It’s the case in Math that sets don\u2019t have to only be finite groups, they can also be infinite.\n There is set notation that can make presenting sets a little bit easier and shorter, particularly for cases where sets are infinite.<\/p>\n Which means that we have a set in which the letter y<\/b><\/i><\/font> can be any number, but it must be greater than 7<\/b>.\n With Math sets and subsets, a set J<\/font> can be a ‘subset’ of another set K<\/font>.\n In this situation, set J<\/font> is a subset of set K<\/font>.\n With sets in Math, the ‘complement’ of a set, is the elements that are NOT<\/u> part of that set.\n The union of two sets is the set of elements that are in either set M<\/font> or<\/u> in set N<\/font>.\n
\nIn set notation, the common notation for a set, is a collection of elements inside curly brackets, separated by commas.\n
\nFor example, { 1 , 2 , 3 , 4<\/font> }<\/b>.\n
\nThe letters from A<\/font> to E<\/font> can also be a set.\n
\n{ A , B , C , D , E<\/font> }<\/b>\n
\nThe set order doesn’t matter, { B , D , C, A , E<\/font> }<\/b> is still the same set.<\/p>\n
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\n\n\n\nSets and Set Notation, Further<\/span><\/h2>\n\n\n\n
\nWe could have a situation where we have 2 sets, A<\/font> and B<\/font>.\n
\nA<\/font> = { 10 , 11 , 12 , 13 , 14<\/font> }<\/b>\n
\nB<\/font> = { 15 , 16 , 17 , 18 , 19<\/font> }<\/b>\n
\nThe number 11<\/b> is a member of set A<\/font>. This would be denoted by 11<\/font> ∈<\/b> A<\/font>.\n
\n∈<\/font><\/b> = \u201cis a member\/element of\u201d.\n
\nAs can be seen, it\u2019s also the case that 17<\/font> ∈<\/b> B<\/font>.\n
\nBut, the number 12<\/b> is NOT<\/u> an element of the set B<\/font>,\n
\nlikewise the number 16<\/b> is NOT<\/u> an element of the set A<\/font>.\n
\nThese cases can be denoted by 12 ∉<\/b> B<\/font><\/font> and 16 ∉<\/b> B<\/font><\/font>.\n
\n∉<\/font><\/b> = \u201cis NOT a member\/element of\u201d.\n
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\nWhen this happens, such a set is known as the empty set { }, which is denoted by the symbol ∅<\/b>.<\/p>\n
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\n\n\n\nFinite and Infinite Sets<\/span><\/h2>\n\n\n\n
\nFor instance, we could have a set that is all whole numbers larger than 10<\/b>.<\/p>\n{ 11 , 12, 13 , …. }<\/b>\n
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\nA set for all the numbers greater in size than 7<\/b> can be denoted as: { y<\/i><\/font> | y<\/i><\/font> > 7 }<\/b>.\n
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\nA handy page with some good examples set notation is available to view at the Mathwords<\/i><\/u><\/font><\/a> website.<\/font><\/p>\n
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\n\n\n\nMath Sets and Subsets,
Set Compliment<\/span><\/h2>\n\n\n\n
\n\n\n\nSets and Subsets:<\/span><\/h3>\n\n\n\n
\nIf it happens to be the case that all of the elements that are in set J<\/b>, are elements that are also in set K<\/b>.<\/p>\n
\nWe can look at 2<\/font> sets.\n
\nJ<\/font> = { 3, 12 , 24 }<\/b> K<\/font> = { 3 , 8 , 12 , 24 , 35 }<\/b>\n
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\nThe notation for this is J<\/font> ⊂ K<\/font>.<\/p>\n
\n\n\n\nSet Compliment:<\/span><\/h3>\n\n\n\n
\nIf a set is labelled as A<\/font>, the notation for the compliment would be A<\/font>c<\/font><\/sup>.<\/p>\n
\nBut also, when you have 2 separate sets, there can be another set that is either:\n
\nSet J<\/font> minus<\/i> Set K<\/font>, or<\/u> Set J<\/font> minus<\/i> Set K<\/font>.\n
\nThe notation for which is a backslash between the set labels.<\/font>\n
\nJ\\K<\/font> = Elements in J<\/font>, but not in K<\/font>.\n
\nK\\J<\/font> = Elements in K<\/font>, but not in J<\/font>.\n
\nThus for the sets J<\/font> and K<\/font> here, the set K\\J<\/font> is:\n
\n{ 8 , 35 }<\/b>.\n
\nAs 8<\/b> and 35<\/b> are in set K<\/font>, but NOT<\/u> in set J<\/font>.\n
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\n\n\n\nMath Sets and Subsets,
Intersection and Union<\/span><\/h2>\n\n\n\n
\nIf we had two sets denoted as M<\/font> and N<\/font>.\n
\nThe ‘intersection’ of both sets, is the set of elements in both set M<\/font> and set N<\/font>.\n
\nThe notation for which is M ∩ N<\/font>.\n
\nIf we have 2 sets:\n
\nM<\/font> = { 11 , 2 , 7 , 65 , 14 }<\/b>\n
\nN<\/font> = { 9 , 2 , 71 , 65 , 14 }<\/b>\n
\nThen the set M ∩ N<\/font> = { 2 , 14 , 65 }<\/b>.\n
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\nThe notation for which is M∪N<\/font>.<\/p>\nThe set M<\/font> ∪ N<\/font><\/b> = { 2 , 7 , 9 , 11 , 14 , 65 , 71 }<\/b>.\n
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