If G is a simple graph, the vector space of g is the vector space over the field Z2 of integers modulo 2, whose elements are subsets of E (G). The sum is E+F of two subsets E and F is the set odd edges in E or F but not both, and scalar multiplication is defined by1×E=E and 0xE=∅. Show that this defines a vector space over Z2 and find the basis of it.

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