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LOGIC SIMPLIFICATION USING BOOLEAN ALGEBRA • The most obvious way to simplify Boolean expressions is to manipulate them in the same way as normal algebraic expressions are manipulated. • With regards to logic relation in

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Subspace: A subset W of a vector space V over a field F is called a subspace of V if W is a vector space over F with the operations of additions and scalar multiplication defined on V. Let V be a vector space and W a subset of V. Then W is a subspace of V if and only if the following three conditions hold for the operations defined in V. a) 0 in W b) x + y in W whenever x, y in W c) cx in W whenever c in F and x in W W inherits all of the other axioms too, and it in itself is a vector space. Linear combination of vectors: Let V be a vector space and S a nonempty subset of V. A vector v in V is called a linear combination of vectors of S if there exist a finite number of vectors u1, u2, un in S and scalars a1, a2, an in F such that v = a1u1 + a2u2 + anun. In this case, we also say that v is a linear combination of u1, u2, un and call a1, a2, an the coefficients of the linear combination. Span of a set of vectors: Let S be a nonempty subset of a vector space V. The span of S, denoted span(S), is the set consisting of all linear combinations of the vectors in S. The span of any subset S of a vector space V is a subspace of V. Moreover, any subspace of V that contains S must also contain the span of S. A subset S of a vector space V generates (or spans) V if span(S) = V. In this case, we also say that the vectors of S generate (or span) V. Basis of a subspace: A basis B for a vector space V is a linearly independent subset of V that ge

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