Prove that - = − / B
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(-a) =(-1)*a by definition
(-b) =(-1)*b by definition
(-a)*(-b) = (-1)*a*(-1)*(b) = (-1)*(-1)*a*b commutative law
= ((-1)*(-1))*(a*b) by associative law
(-1)*(-1) = 1, a*b = ab by definition
1*ab = ab by definition
(-a)*(-b) = ab. Q.E.D.
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