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Fraction rules A B C vs B C A - Mathematics Stack Exchange You may have been confused by the implied parentheses in the size of the fraction bars Your first rule is $$\frac A{\left(\frac BC\right)}=\frac {AC}B$$ which you can establish by multiplying the fraction by $\frac CC$
When is $(a^b)^c $ = $a^{bc}$ true? - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
I cant simplify this A’B’C - Mathematics Stack Exchange I have to get this expression A’B’C + A’BC + A’BC’ + AB’C + ABC to A'B+C I did this but I can't finish it, I don't know how to A’B’C + A’BC + A’BC’ + AB’C + ABC A'B(C+C')+C(A'B'+AB'+AB) A'B+C(A'B'+AB'+AB) That's it, I don't know how to solve that
elementary set theory - Prove or disprove: $A-(B-C) = (A-B)-C . . . Let X <=Y if x is a subset of Y Note if X<=Y, Z-X>=Z-Y B-C <=B Thus A-(B-C)>=A-B A-(B-C)-nullset>=A-B-C similarly It is easily shown when we have one strict inequality between B-C and B or the nullset and C our final inequality is strict and the theorem fails When we have no such strict inequality by antisymmetry of <= the equation holds
AC + BC in boolean algebra - Mathematics Stack Exchange I am trying to understand the simplification of the boolean expression: AB + A'C + BC I know it simplifies to A'C + BC And I understand why, but I cannot figure out how to perform the simplific
elementary set theory - Proof of $(A - B) - C = A - (B \cup C . . . (A-B)-C=A-(B ∪ C) The right hand side means A ∩ (B ∪ C)^c (c means compliment) Which, in turn, means, by deMorgan's law A ∩ B^c ∩ C^c Hence, by the associative property, (A ∩ B^c) ∩ C^c And, reinstating the minus sign, (A-B)-C Thus (A-B)-C=A-(B ∪ C)
How does ABC + ABC + ABC simplify to (A + B)C? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers