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kritisachan
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A set S contains the following 5 elements: S = (p,q,r,x,y). How many 24 Jun 2023, 08:28
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55% (hard)

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58% (01:32) correct 42% (01:46) wrong based on 151 sessions

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A set S contains the following 5 elements: S = (p,q,r,x,y). How many subsets of this set S are possible that contain both x and y?

A. 6
B. 8
C. 7
D. 11
E. 12
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B
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Bunuel
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A set S contains the following 5 elements: S = (p,q,r,x,y). How many 24 Jun 2023, 08:44
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kritisachan
A set S contains the following 5 elements: S = (p,q,r,x,y). How many subsets of this set S are possible that contain both x and y?

A. 6
B. 8
C. 7
D. 11
E. 12
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So, we are need to find the number of the subsets that contain both x and y: {x, y, ...}. Each of the three remaining elements p, q, and r have two possibilities: they can either be included in the subset or not. Hence, the number of subsets that include both x and y is 2*2*2 = 8.

Answer: B.
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A set S contains the following 5 elements: S = (p,q,r,x,y). How many 24 Jun 2023, 10:33
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Bunuel
kritisachan
A set S contains the following 5 elements: S = (p,q,r,x,y). How many subsets of this set S are possible that contain both x and y?

A. 6
B. 8
C. 7
D. 11
E. 12

So, we need to find the number of the subsets that contain both x and y: {x, y, ...}. Each of the three remaining elements p, q, and r have two possibilities: they can either be included in the subset or not. Hence, the number of subsets that include both x and y is 2*2*2 = 8.

Answer: B.
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Hi Bunuel,

Can you please elaborate on the part "Each of the three remaining elements p, q, and r have two possibilities: they can either be included in the subset or not."?

Thanks in advance. :)
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A set S contains the following 5 elements: S = (p,q,r,x,y). How many 24 Jun 2023, 12:20
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Bunuel
kritisachan
A set S contains the following 5 elements: S = (p,q,r,x,y). How many subsets of this set S are possible that contain both x and y?

A. 6
B. 8
C. 7
D. 11
E. 12

So, we need to find the number of the subsets that contain both x and y: {x, y, ...}. Each of the three remaining elements p, q, and r have two possibilities: they can either be included in the subset or not. Hence, the number of subsets that include both x and y is 2*2*2 = 8.

Answer: B.



Hi Bunuel,

Can you please elaborate on the part "Each of the three remaining elements p, q, and r have two possibilities: they can either be included in the subset or not."?

Thanks in advance. :)
Show more

For each of the remaining elements p, q, and r, there are two options: either we put it in the subset or we don't. So, for three elements, we have 2 (either in or not) times 2 (again, either in or not) times 2 (same thing), which equals 8. This means there are 8 possible subsets that include x and y.
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A set S contains the following 5 elements: S = (p,q,r,x,y). How many 30 Aug 2025, 12:00
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