Can somebody help me understand the question from the set theory?
$begingroup$
Multiple choice question.
Let $A_1, A_2,ldots A_m$ be $m$ sets such that $O(A_i)=p forall i= 1,2,ldots,m$ and $B_1, B_2,ldots ,B_n$ be $n$ sets such that $O(B_i)=q forall i= 1,2,...,n$. If $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$ and each element of $S$ belongs to exactly $alpha$ number of $A_i$'s and $beta$ number of $B_j$'s, then
1)$pm=nq$
2)$alpha pm = beta nq$
3)$beta pm = alpha nq$
4)$(pm)^alpha = (nq)^beta$
The answer is 3.
I don't understand what is being asked in the question and how to solve it. Can somebody help with that?
elementary-set-theory
edited Jan 1 at 15:17
Dorian Gray
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
$endgroup$
add a comment |
$begingroup$
Multiple choice question.
Let $A_1, A_2,ldots A_m$ be $m$ sets such that $O(A_i)=p forall i= 1,2,ldots,m$ and $B_1, B_2,ldots ,B_n$ be $n$ sets such that $O(B_i)=q forall i= 1,2,...,n$. If $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$ and each element of $S$ belongs to exactly $alpha$ number of $A_i$'s and $beta$ number of $B_j$'s, then
1)$pm=nq$
2)$alpha pm = beta nq$
3)$beta pm = alpha nq$
4)$(pm)^alpha = (nq)^beta$
The answer is 3.
I don't understand what is being asked in the question and how to solve it. Can somebody help with that?
elementary-set-theory
edited Jan 1 at 15:17
Dorian Gray
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
$endgroup$
1
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20
add a comment |
$begingroup$
Multiple choice question.
Let $A_1, A_2,ldots A_m$ be $m$ sets such that $O(A_i)=p forall i= 1,2,ldots,m$ and $B_1, B_2,ldots ,B_n$ be $n$ sets such that $O(B_i)=q forall i= 1,2,...,n$. If $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$ and each element of $S$ belongs to exactly $alpha$ number of $A_i$'s and $beta$ number of $B_j$'s, then
1)$pm=nq$
2)$alpha pm = beta nq$
3)$beta pm = alpha nq$
4)$(pm)^alpha = (nq)^beta$
The answer is 3.
I don't understand what is being asked in the question and how to solve it. Can somebody help with that?
elementary-set-theory
edited Jan 1 at 15:17
Dorian Gray
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
$endgroup$
Multiple choice question.
Let $A_1, A_2,ldots A_m$ be $m$ sets such that $O(A_i)=p forall i= 1,2,ldots,m$ and $B_1, B_2,ldots ,B_n$ be $n$ sets such that $O(B_i)=q forall i= 1,2,...,n$. If $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$ and each element of $S$ belongs to exactly $alpha$ number of $A_i$'s and $beta$ number of $B_j$'s, then
1)$pm=nq$
2)$alpha pm = beta nq$
3)$beta pm = alpha nq$
4)$(pm)^alpha = (nq)^beta$
The answer is 3.
I don't understand what is being asked in the question and how to solve it. Can somebody help with that?
elementary-set-theory
elementary-set-theory
edited Jan 1 at 15:17
Dorian Gray
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
edited Jan 1 at 15:17
Dorian Gray
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
edited Jan 1 at 15:17
Dorian Gray
1032
edited Jan 1 at 15:17
Dorian Gray
1032
edited Jan 1 at 15:17
Dorian Gray
1032
1032
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
asked Jan 1 at 15:03
Karan KumarKaran Kumar
12
12
1
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20
add a comment |
1
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20
1
1
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The question is, which of the statements 1 - 4 follow directly from the conditions.
You could start by determing $O(S)$: Look at $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$
If all $A_i$ and $B_i$ would be disjoint (that is, $alpha=beta=1$), it would be $O(S)=mp=nq$ (essentially answer 1). Now consider other $alpha, beta$.
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
$endgroup$
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
add a comment |
Your Answer
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
The question is, which of the statements 1 - 4 follow directly from the conditions.
You could start by determing $O(S)$: Look at $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$
If all $A_i$ and $B_i$ would be disjoint (that is, $alpha=beta=1$), it would be $O(S)=mp=nq$ (essentially answer 1). Now consider other $alpha, beta$.
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
$endgroup$
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
add a comment |
$begingroup$
The question is, which of the statements 1 - 4 follow directly from the conditions.
You could start by determing $O(S)$: Look at $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$
If all $A_i$ and $B_i$ would be disjoint (that is, $alpha=beta=1$), it would be $O(S)=mp=nq$ (essentially answer 1). Now consider other $alpha, beta$.
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
$endgroup$
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
add a comment |
$begingroup$
The question is, which of the statements 1 - 4 follow directly from the conditions.
You could start by determing $O(S)$: Look at $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$
If all $A_i$ and $B_i$ would be disjoint (that is, $alpha=beta=1$), it would be $O(S)=mp=nq$ (essentially answer 1). Now consider other $alpha, beta$.
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
$endgroup$
The question is, which of the statements 1 - 4 follow directly from the conditions.
You could start by determing $O(S)$: Look at $bigcup^n_{i=0} A_i =bigcup^n_{i=0} B_i=S$
If all $A_i$ and $B_i$ would be disjoint (that is, $alpha=beta=1$), it would be $O(S)=mp=nq$ (essentially answer 1). Now consider other $alpha, beta$.
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
answered Jan 1 at 15:23
Dorian GrayDorian Gray
1032
1032
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
add a comment |
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
When it says each element of S belongs to exactly α number of Ai's and β number of Bj's. What does it mean and what does $alpha$ and $beta$ represent?
$endgroup$
– Karan Kumar
Jan 1 at 15:40
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
$begingroup$
Exactly what is written there. If you pick a $sin S$ at random, there are exactly $beta$ indices $i_1,ldots,i_beta$ so that $sin B_{i_1},ldots,B_{i_beta}$.
$endgroup$
– Dorian Gray
Jan 1 at 16:01
add a comment |
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1
$begingroup$
Where is this question coming from?
$endgroup$
– user458276
Jan 1 at 15:20