Set theory was developed by mathematicians to be able to talk about collections of objects. It has turned out to be an invaluable tool for defining some of the most complicated mathematical structures.
Let us explore few common Set theory symbols used in more complicated math structures.
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 âˆª B | union | objects that belong to set A or set B | A âˆª B = {1, 7, 9, 13, 15, 21, 23} |
A âˆ© B | intersection | objects that belong to both the sets, A and B | A âˆ© B = {7, 13, 15 } |
A âŠ† B | subset | subset has few or all elements equal to the set | {7, 15} âŠ† {7, 13, 15, 21} |
A âŠ„ B | not subset | left set not a subset of right set | {1, 23} âŠ„ B |
A âŠ‚ B | proper subset / strict subset | subset has fewer elements than the set | {7, 13, 15} âŠ‚ {1, 7, 9, 13, 15, 23} |
A âŠƒ B | proper superset / strict superset | set A has more elements than set B | {1, 7, 9, 13, 15, 23} âŠƒ {7. 13. 15. } |
A âŠ‡ B | superset | set A has more elements or equal to the set B | {1, 7, 9, 13, 15, 23} âŠƒ {7. 13. 15. 21} |
Ã˜ | empty set | Ã˜ = { } | C = {Ã˜} |
P (C) | power set | all subsets of C | C = {4,7},
P(C) = {{}, {4}, {7}, {4,7}} Given by \(2^{s}\), s is number of elements in set C |
A âŠ… B | not superset | set A is not a superset of set B | {1, 7, 9, 13, 15, 23} âŠ…{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} |
Ac | complement | all the objects that do not belong to set A | We know, U = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}
Ac = {2, 21, 28, 30} |
A âˆ† B | symmetric difference | objects that belong to A or B but not to their intersection | A âˆ† B = {1, 9, 21, 23} |
aâˆˆB | element of | set membership | B = {7, 13, 15, 21},
13 âˆˆ B |
(a,b) | ordered pair | collection of 2 elements | |
xâˆ‰A | not element of | no set membership | A = {1, 7, 9, 13, 15, 23, 5 âˆ‰ A |
|B|, #B | cardinality | the number of elements of set B | B = {7, 13, 15, 21}, |B|=4 |
AÃ—B | cartesian product | set of all ordered pairs from A and B | {3,5} Ã— {7,8} = {(3,7), (3,8), (5,7), (5, 8) } |
\(\mathbb{N}\) | natural numbers / whole numbers Â set (without zero) | \(\mathbb{N}\)1 = {1,2,3,4,5,…} | 6 âˆˆ \(\mathbb{N}\)1 |
\(\mathbb{N}\)0 | natural numbers / whole numbers Â set (with zero) | \(\mathbb{N}\)0 = {0,1,2,3,4,…} | 0 âˆˆ \(\mathbb{N}\)0 |
\(\mathbb{Q}\) | rational numbers set | \(\mathbb{Q}\)= {x | x=a/b, a,bâˆˆ\(\mathbb{Z}\)} | 2/6 âˆˆ \(\mathbb{Q}\) |
\(\mathbb{Z}\) | integer numbers set | \(\mathbb{Z}\)= {…-3,-2,-1,0,1,2,3,…} | -6 âˆˆ \(\mathbb{Z}\) |
\(\mathbb{C}\) | complex numbers set | \(\mathbb{C}\)= {z | z=a+bi, -âˆž<a<âˆž, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â -âˆž<b<âˆž} | 6+2i âˆˆ \(\mathbb{C}\) |
\(\mathbb{R}\) | real numbers set | \(\mathbb{R}\)= {x | -âˆž < x <âˆž} | 6.343434 âˆˆ\(\mathbb{R}\)< |