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# Notation - Some mathematical notation used in Math 375 Set...

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Some mathematical notation used in Math 375 Set notation Examples: { x : x R , x > 4 } , or also { x R : x > 4 } , denotes the set of all real numbers which are greater than 4. x E means the element x belongs to the set E . x / A means the element x does not belong to E . If E = { x R : x > 4 } , then 5 E but 3 / E . For two sets E , F we write E F if E is a subset of F , that is if every element of E also belongs to F . E F is the intersection of E and F , that is the set which consists of those x which belongs to both E and F . E F is the union of E and F , that is the set which consists of those x which belongs to either E or F or both. is the empty set which does not have any members. Observe that the empty set is a subset of every set. Implications: Let A and B to statements. A = B ” means “ A implies B ” (in other words this means: If A holds, then B holds true). An alternative (more precise but less intuitive) form of expressing A = B is as follows A = B is true if either A is false or A

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