MHB -aux.01 Venn diagram universal set U and sets A and B.

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The discussion focuses on the calculation of the probability of the union of sets B and the complement of set A, denoted as B ∪ A'. The participants confirm that the ratio of the size of this union to the universal set U is 35 out of 100, simplifying to 7 out of 20. The calculations are verified as correct, emphasizing the accuracy of the probability representation. The conversation highlights the importance of understanding set operations in probability theory. Overall, the discussion effectively clarifies the relationship between the sets involved.
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so I have $B\cup A'$

(c)
$\displaystyle\frac{n(B\cup A')}{n(U)}=\frac{35}{100}=\frac{7}{20}$
 
karush said:
so I have $B\cup A'$

(c)
$\displaystyle\frac{n(B\cup A')}{n(U)}=\frac{35}{100}=\frac{7}{20}$

That is correct. :D
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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