Union, intersection, differences and symmetric difference of two sets of numbers or words, with the Jaccard index and a Venn diagram.
અપડેટ કરેલું તપાસેલાં ઉદાહરણો: 6
A and B share 2 of the 7 distinct items (Jaccard index 0.2857); 3 are only in A and 2 only in B.
Jaccard index: 2 / 7 = 0.285714.
The calculator treats each list as a set, dropping repeats, and compares the two. The union A ∪ B holds everything in either set, the intersection A ∩ B what is in both, the differences A − B and B − A what is in one but not the other, and the symmetric difference A △ B what is in exactly one. The Jaccard index |A ∩ B| ÷ |A ∪ B| scores the overlap from 0 for disjoint sets to 1 for identical ones.
Comparing customer or email lists, finding shared tags, checking what one version of a list adds or removes, and discrete-mathematics homework are typical uses. The default sets {1, 2, 3, 4, 5} and {4, 5, 6, 7} share 2 of their 7 distinct items, so the Jaccard index is 2/7 ≈ 0.2857.
Items can be numbers or words, separated by commas, semicolons, new lines or spaces. Numbers are compared by value, so 1 and 1.0 are one item; words must match exactly, including capital letters. Results list numbers in order, then words alphabetically.
ચકાસણીનો સ્ત્રોત: Python set operators |, &, -, ^ on {1,2,3,4,5} and {4,5,6,7}; 2/7 = 0.285714
ચકાસણીનો સ્ત્રોત: Python set operators on string sets, sorted()
ચકાસણીનો સ્ત્રોત: Python: {1,3,5} & {2,4,6} == set()
ચકાસણીનો સ્ત્રોત: Python: {Decimal('1'), Decimal('1.0'), Decimal('2')} has 2 elements; Decimal('2.00') == Decimal('2')
The union A ∪ B contains every element in A, in B or in both; the intersection A ∩ B contains only the elements in both. For A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, the union is {1, 2, 3, 4, 5, 6, 7} and the intersection is {4, 5}. The union is never smaller than either set, and the intersection never larger.
The elements that are in exactly one of the two sets: A △ B = (A − B) ∪ (B − A), which is the union with the intersection removed. For {1, 2, 3, 4, 5} and {4, 5, 6, 7} it is {1, 2, 3, 6, 7}. It behaves like XOR in logic, and Python's ^ operator computes it for sets.
Use the inclusion–exclusion principle: |A ∪ B| = |A| + |B| − |A ∩ B|, subtracting the intersection because its elements were counted twice. With |A| = 5, |B| = 4 and |A ∩ B| = 2, the union has 5 + 4 − 2 = 7 elements. For three sets it extends to |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| + |A ∩ B ∩ C|.
A similarity score for two sets: the size of their intersection divided by the size of their union, from 0 for disjoint sets to 1 for identical ones. {1, 2, 3, 4, 5} and {4, 5, 6, 7} share 2 of 7 distinct items, a Jaccard index of 2/7 ≈ 0.2857. It is used to compare documents, tag sets and search results, and 1 minus the index is the Jaccard distance.
No. A − B, also written A \ B, keeps the elements of A that are not in B, while B − A keeps the elements of B that are not in A. With A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, A − B = {1, 2, 3} but B − A = {6, 7}. The two differences never share an element, and together they form the symmetric difference.
ચોકસાઈ તમારા ઇનપુટ અને પદ્ધતિની ધારણાઓ પર આધારિત છે. દશાંશ ગણતરી 50 સાર્થક અંકો વાપરે છે, પરંતુ અંદાજ, સંખ્યાત્મક પદ્ધતિઓ અને મૂળ ડેટા ઓછા ચોક્કસ હોઈ શકે છે; દર્શાવેલા મૂલ્યોને રાઉન્ડ કરવાથી આ મર્યાદાઓ દૂર થતી નથી. સ્વતંત્ર સ્ત્રોતોના ઉકેલેલા ઉદાહરણો સાથે ચકાસણી: 6. ઉદાહરણ તરીકે, “{1, 2, 3, 4, 5} and {4, 5, 6, 7}”ને Python set operators |, &, -, ^ on {1,2,3,4,5} and {4,5,6,7}; 2/7 = 0.285714 સાથે ચકાસવામાં આવે છે.
Wolfram MathWorld — Union, Intersection, Set Difference, Symmetric Difference; Python documentation — set types and operations.
આ કેલ્ક્યુલેટરમાં સ્વતંત્ર સ્રોતોના જવાબો ધરાવતા 6 ઉકેલેલાં ઉદાહરણો છે. તે પરીક્ષણ સમૂહમાં ચાલે છે અને તમે અહીં પણ ચલાવી શકો છો.