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Fraction rules A B C vs B C A - Mathematics Stack Exchange You have written the second the same way on the left, B (C A) = B CA B (C A) = B C A which is incorrect I suspect you meant to write (B C) A = B CA (B C) A = B C A which is correct and can be established by multiplying by C C C C The only clue in what you wrote is the size of the fraction bars and your top one is the largest in both cases
When is $(a^b)^c $ = $a^{bc}$ true? - Mathematics Stack Exchange It is true when a> 0 a> 0 and b, c ∈R b, c ∈ R In this situation we have a canonical choice for a value for ab a b, given by eb ln a e b ln a, using the principal branch of the natural logarithm on positive real numbers (that is, the one that gives ln a ∈R ln a ∈ R) For other values of a a there is no natural choice for ln a ln a, so ab a b has multiple equally valid answers What is
Simplification of: AB + AC + BC in boolean algebra 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
Factoring $(a+b)(a+c)(b+c)=(a+b+c)(ab+bc+ca)-abc$ How to prove the following equality? $$(a+b)(a+c)(b+c)=(a+b+c)(ab+bc+ca)-abc$$ I did it $$\\begin{aligned} a^2b + a^2c + ab^2 + cb^2 + bc^2 + ac^2 + 2abc amp;=a^2(b
discrete mathematics - Prove: $A × (B ∩ C) = (A × B) ∩ (A × C . . . You need to "element chase"; that is, suppose (x, y) ∈ A × (B ∩ C) (x, y) ∈ A × (B ∩ C) and then show you must have (x, y) ∈ (A × B) ∩ (A × C) (x, y) ∈ (A × B) ∩ (A × C), then do the other direction as well I'll do one direction for you and you can try the other yourself Suppose (x, y) ∈ A × (B ∩ C) (x, y) ∈ A × (B ∩ C) Then x ∈ A x ∈ A and y ∈ B ∩ C
Prove A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) [duplicate] Hint If X ∈ A X ∈ A and X ∈ B X ∈ B, then X ∈ A ∩ B X ∈ A ∩ B Otherwise, then X ∈ A X ∈ A and X ∈ C X ∈ C, so X ∈ A ∩ C X ∈ A ∩ C Either way, X ∈ (A ∩ B) ∪ (A ∩ C) X ∈ (A ∩ B) ∪ (A ∩ C) But this doesn't complete the proof, since we've only shown inclusion in one direction Can you do the other?
I cant simplify this A’B’C - Mathematics Stack Exchange Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience Here are helpful tips to write a good question and write a good answer For equations, please use MathJax