A collected of well defined objects is called a set.
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Boolean algebra deals with logic and truth as it pertains to sets and possibilities. It uses the and, or and not operators to set up truth tables to define if a statement is true or not.
No, because equivalent sets are sets that have the SAME cardinality but equal sets are sets that all their elements are precisely the SAME. example: A={a,b,c} and B={1,2,3} equivalent sets C={1,2,3} and D={1,2,3} equal sets
3,4,5 1,2,3 these are sets of pythagorean triples
There is quite a lot of algebra devoted to solving problems involving sets, parts of sets, and concepts closely related to sets, such as subsets, cosets, and groups. You'll need to be more specific.
Sets contain elements. The intersection of sets (represented by an upside-down 'U') is the list of elements that are common in both sets. The union of sets (represented by 'U') is the list of all the elements in the relevant sets. E.g. If A={a,b,c,d,e,f} and B={a,e,i,o,u}: The intersection of A and B is {a,e}. The union of A and B is {a,b,c,d,e,f,i,o,u} (notice how repeating elements, e.g. 'a' and 'e', are only listed once even though they occur in both sets.)