Set theory

Set theory

Set theory was developed to explain about collections of objects, in Maths. Basically, the definition states it is a collection of elements. These elements could be numbers, alphabets, variables, etc. The notation and symbols for sets are based on the operations performed on them. You must have also heard of subset and superset, which are the counterpart of each other.

Symbols Used For Representation of Sets

Let us see the different types of symbols we used while we learn about sets. Consider a Universal set (U) = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {1, 7, 9, 13, 15, 23}, B = {7, 13, 15, 21}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {1, 7, 9, 13, 15, 21, 23}
A ∩ B	intersection	objects that belong to both the sets, A and B	A ∩ B = {7, 13, 15 }
A ⊆ B	subset	subset has few or all elements equal to the set	{7, 15} ⊆ {7, 13, 15, 21}
A ⊄ B	not subset	left set not a subset of right set	{1, 23} ⊄ B
A ⊂ B	proper subset / strict subset	subset has fewer elements than the set	{7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23}
A ⊃ B	proper superset / strict superset	set A has more elements than set B	{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. }
A ⊇ B	superset	set A has more elements or equal to the set B	{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. 21}
Ø	empty set	Ø = { }	C = {Ø}
P (C)	power set	all subsets of C	C = {4,7}, P(C) = {{}, {4}, {7}, {4,7}} Given by 2s, s is number of elements in set C
A ⊅ B	not superset	set A is not a superset of set B	{1, 7, 9, 13, 15, 23} ⊅{7, 13, 15, 21}
A = B	equality	both sets have the same members	{7, 13,15} = {7, 13, 15}
A \ B or A-B	relative complement	objects that belong to A and not to B	{1, 9, 23}