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Sets and operations
Membership, subsets, union, intersection, complement, and Venn diagrams.
A set is a collection; the operations combine them: union (either), intersection (both), difference, complement. Picture it: a Venn diagram; each region is a combination of memberships. Think it: the operations satisfy the same laws as and/or/not, sets and logic are the same algebra (Boolean algebra).
उदाहरण · {1,2,3,4} union {3,4,5,6}
{1,2,3,4} union {3,4,5,6}
चरणद्वारा चरण
- A = \left\{1, 2, 3, 4\right\},\quad B = \left\{3, 4, 5, 6\right\}
The two sets.
- A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}
Keep everything in either set.
- |A| = 4,\ |B| = 4,\ |A \cup B| = 6
Cardinalities. Note |A ∪ B| = |A| + |B| − |A ∩ B|.
जवाफ प्रकट गर्नुहोस्
अब तपाईँ समस्या रोज्नुहोस्, वा टाइप गर्नुहोस् वा तपाईँको आफ्नै रेखाचित्र गर्नुहोस् । प्रत्येक चरण, एउटा तस्वीर, तपाईँले सोध्नु अघि उत्तर लुकेको छ ।
एक निःशुल्क खाता प्रत्येक पाठ मा नोट थप्छ, तपाईं के समाप्त गरेको छ को एक रेकर्ड, एक ठाउँमा आफ्नो समाधान समस्या, र एक शिक्षक तपाईं यो पृष्ठ बारेमा सोध्न सक्नुहुन्छ. गणित आफैलाई सबैलाई खुला छ, मा साइन इन वा छैन.
साइन अप गर्नुहोस् लगइनयहाँ प्रयोग गरिएको प्रतीक
पूर्ण परिभाषा, एउटा तस्वीर, र यो प्रत्येक अक्षर अर्थ के लागि कुनै पनि प्रतीक ट्याप गर्नुहोस्।
कसरी: Sets and operations
- Write each set explicitly, or describe it by a property.
- For a union keep everything in either; for an intersection only what is in both.
- Check |A ∪ B| = |A| + |B| − |A ∩ B|.
प्रश्नहरू मानिसहरूले सोध्छन्
Are some infinities bigger than others?
Yes. The integers and the rationals can be listed; the real numbers cannot (Cantor's diagonal argument), so there are strictly more reals than integers.
What is the difference between a relation and a function?
A relation pairs inputs with outputs freely; a function is a relation in which every input gets exactly one output.
यसमा थप Set Theory & Logic
Relations, functions and equivalenceCardinality and infinityLogic and methods of proof