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08 Jul 2024, 02:52
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
66% (01:46) correct
34%
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wrong
based on 270
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The set {s, t, u} has the subsets {s}, {t}, {u}, {s,t}, {s,u}, {t,u}, {s,t,u} and {} - empty set. What is the number of the subsets of set {s,t,u,v,w} that must be exclude element t and include element u?
A. 2
B. 4
C. 8
D. 16
E. 32
A. 2
B. 4
C. 8
D. 16
E. 32
08 Jul 2024, 18:55
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sahilsah456
A straight formula for such questions is \(2^{number \ \ of \ \ element \ \ in \ \ the \ \ set}\).
The number of the subsets of set {s,t,u,v,w} that must be exclude element t and include element u: So exclude both t and u. We are left with {s, v, w} and total number of ways = \(2^3\) or 8.
Let us find the solution by calculating.
We cannot include t, so we are left with {s,u,v,w}.
Next, u is always there, so {u, X}. This X would be combination of the remaining.
1) Only one element: {u}, here X is null.
2) Only two element: {u, X}, choose X as any one of the remaining elements, so 3C1 or 3 ways. => {u, s}, {u, v}, {u, w}
3) Only three element: {u, X}, choose X as any two of the remaining elements, so 3C2 or 3 ways. => {u, s, v}, {u, v, w}, {u, s, w}
4) Only four element: {u, X}, choose X as any three of the remaining element, so 3C3 or 1 way. => {u, s, v, w}
Total = 1+3+3+1 = 8
C
17 Jul 2024, 07:56
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chetan2u
why did u exlcude u from the 2^3 formule the questions asks u to include u and exclude t so why do we exclude u while calculating using the formulae ???? please explain
