Explanation of Set Identity $(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$De Morgan's law on...
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Explanation of Set Identity $(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$
De Morgan's law on infinite unions and intersectionsWhat is the probability in this case?Does $A cap (E_1cup E_2) = [Acap E_1]cup [Acap E_2cap E_1^c]$?Set equality $A cap (E_1 cup E_2) cap E_3 = A cap E_3$ if $cap E_k = emptyset$Probability of 1 trial getting 8 or more heads/tails in 10 trials of 10 flipsNumber of ways to place 4 different letters into 4 different envelopes.How come the proportion of heads to tails across a large number of coin flips tend toward $1:1$ if all outcomes are equally likely?Expected number of coin flips until a random number of consecutive headsIf $…E_3subset E_2 subseteq E_1$ and $mu(E_i)<infty$ then $mu(cap E_n)=lim(mu(E_n))$Dividing a deck in four stacks, aces must be in different piles (Conditional Prob.)
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I ran across the following set identity in a probability problem:
$$(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$$ and can't make heads or tails of it. I tried applying De Morgan's law as follows:
$$ (E_1 E_2 E_3)^c = E_1^c cup E_2^c cup E_3^c$$
but don't see how this helps. I am not necessarily looking for a proof of the identity, but rather a way to understand heuristically why it is true, although a proof would probably help with that.
probability elementary-set-theory
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
$endgroup$
add a comment |
$begingroup$
I ran across the following set identity in a probability problem:
$$(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$$ and can't make heads or tails of it. I tried applying De Morgan's law as follows:
$$ (E_1 E_2 E_3)^c = E_1^c cup E_2^c cup E_3^c$$
but don't see how this helps. I am not necessarily looking for a proof of the identity, but rather a way to understand heuristically why it is true, although a proof would probably help with that.
probability elementary-set-theory
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
$endgroup$
add a comment |
$begingroup$
I ran across the following set identity in a probability problem:
$$(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$$ and can't make heads or tails of it. I tried applying De Morgan's law as follows:
$$ (E_1 E_2 E_3)^c = E_1^c cup E_2^c cup E_3^c$$
but don't see how this helps. I am not necessarily looking for a proof of the identity, but rather a way to understand heuristically why it is true, although a proof would probably help with that.
probability elementary-set-theory
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
$endgroup$
I ran across the following set identity in a probability problem:
$$(E_1 E_2 E_3)^c = E_1 cup (E_1 E_2^c) cup (E_1 E_2 E_3^c)$$ and can't make heads or tails of it. I tried applying De Morgan's law as follows:
$$ (E_1 E_2 E_3)^c = E_1^c cup E_2^c cup E_3^c$$
but don't see how this helps. I am not necessarily looking for a proof of the identity, but rather a way to understand heuristically why it is true, although a proof would probably help with that.
probability elementary-set-theory
probability elementary-set-theory
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
asked Mar 14 at 0:43
Is12PrimeIs12Prime
139113
139113
add a comment |
add a comment |
1 Answer
1
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$begingroup$
A consequcne of your identity is
$$(E_1cap E_2 cap E_3)^c subseteq E_1;$$
do you see a problem?
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
$endgroup$
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
add a comment |
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1 Answer
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1 Answer
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$begingroup$
A consequcne of your identity is
$$(E_1cap E_2 cap E_3)^c subseteq E_1;$$
do you see a problem?
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
$endgroup$
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
add a comment |
$begingroup$
A consequcne of your identity is
$$(E_1cap E_2 cap E_3)^c subseteq E_1;$$
do you see a problem?
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
$endgroup$
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
add a comment |
$begingroup$
A consequcne of your identity is
$$(E_1cap E_2 cap E_3)^c subseteq E_1;$$
do you see a problem?
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
$endgroup$
A consequcne of your identity is
$$(E_1cap E_2 cap E_3)^c subseteq E_1;$$
do you see a problem?
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
answered Mar 14 at 0:47
ncmathsadistncmathsadist
43k260103
43k260103
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
add a comment |
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
1
1
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
$begingroup$
Yes, I see the contradiction here. Thank you, the solution I was looking at came from a less than completely reputable source and I won't be as trusting the next time.
$endgroup$
– Is12Prime
Mar 14 at 0:52
add a comment |
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