2.5 Refer to Exercise 2.4. Use the identities A = A ∩ S and S = B ∪ B and a distributive law to prove that a A=(A∩B)∪(A∩B). b If
B⊂AthenA=B∪(A∩B). c Further, show that ( A ∩ B ) and ( A ∩ B ) are mutually exclusive and therefore that A is the union of two mutually exclusive sets, (A ∩ B) and (A ∩ B). d AlsoshowthatBand(A∩B)aremutuallyexclusiveandifB⊂A,Aistheunionoftwo mutually exclusive sets, B and (A ∩ B)
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Answer:
Option D
Step-by-step explanation:
We are given the following equations -
It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -
First, I swapped the first and third rows.
Leading coefficient of row 2 canceled.
The start value of row 3 was canceled.
Matrix rows 2 and 3 were swapped.
Leading coefficient in row 3 was canceled.
And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -
The positioning of the zeros indicated that there was no solution!
<u><em>Hope that helps!</em></u>