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13 Jun 2019, 00:55
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C
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Difficulty:
45%
(medium)
Question Stats:
66% (01:54) correct
34%
(01:55)
wrong
based on 516
sessions
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If a set has the elements {a, b}, then the subsets of the set are {a}, {b}, {a, b} and { } (the empty subset). The set S is defined as {j, k, m, n}. How many subsets of S have either j or m but not both?
A. 3
B. 4
C. 8
D. 9
E. 12
A. 3
B. 4
C. 8
D. 9
E. 12
14 Jun 2019, 23:33
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mangamma
Formula: If number of terms in a set t = n, Number subsets possible = \(2^n\)
Eg: {a, b} n = 2. Total subsets possible = \(2^2\) = 4
Given Set has 4 terms {j, k, m, n}.
--> Total subsets possible = \(2^4\) = 16
From this subtract the cases when Sets have both j&m and neither j&m
Both j & m are present = {j, m, _, _} = 4 subsets are possible [\(2^2\) or count manually {j, m}, {j, m, k}, {j, m, n}, {j, m, k, n}]
Neither j & m are present = {m, n}. Total subsets possible = \(2^2\) = 4
--> Required subsets = 16 - (4 + 4) = 8
Option C
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General Discussion
13 Jun 2019, 02:31
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The number of subsets with 1 element= 2 [{j}, {m}]
The number of subsets with 2 elements= 1*2+1*2=4 [{j,k}, {j,n}, {m,k}, {m,n}]
The number of subsets with 3 elements= 1*1 + 1*1= 2 [{j,k,n}, {m,k,n}]
Total number of subsets of S have either j or m but not both= 2+4+2=8
The number of subsets with 2 elements= 1*2+1*2=4 [{j,k}, {j,n}, {m,k}, {m,n}]
The number of subsets with 3 elements= 1*1 + 1*1= 2 [{j,k,n}, {m,k,n}]
Total number of subsets of S have either j or m but not both= 2+4+2=8
mangamma
