Math, asked by vk5522, 1 year ago

Of all the nonempty subsets S of { 1, 2, 3, 4, 5, 6, 7}, how many do not contain the number |S|, where |S| denotes the number of elements in S? For example, {3, 4} is one such subset, since it does not contain the number 2.

shalinikumari0peaks2: Answer is 63.

shalinikumari0peaks2: Subset of 6 elements |6| which do not contain 6= 7C6 - 6C5 = 1

shalinikumari0peaks2: Subset of 5 elements |5| which do not contain 5= 7C5 - 6C4 = 6 Subset of 4 elements |4| which do not contain 4= 7C4 - 6C3 = 15 Subset of 3 elements |3| which do not contain 3= 7C3 - 6C2 = 20 Subset of 2 elements |2| which do not contain 2= 7C2 - 6C1 = 15 Subset of 1 element |1| which do not contain 1= 7C1 - 6C0 = 6 Hence, final answer = 1+6+15+20+15+6 = 63

nikhilshedshale97: First set with 1 element: we have to select one element out of 6 elements(2,3,4,5,6,7 excluding 1 because of the rule. This can be done in 6C1 ways.)

nikhilshedshale97: Same applies for selecting two elements out of 6(element 2 is exclude: total ways 6C2.)

nikhilshedshale97: This continue for 3 elements: 6C3, For 4 elements set: 6C4, For 5 elements: 6C5, For 6 elements: 6C6, We can not select set of 7 because if we do element 7 will be included in it(which is not allowed).

nikhilshedshale97: So final answer is: 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6 = 6+15+20+15+6+1= 63

Answers

Answered by Anonymous

Hi,

Here is your answer,

GIVEN DATA

Non-Empty subsets are { 1 , 2, 3 , 4 , 5, 6 , 7 }

So, therefore he total number of subsets are 7.

Now,

n = 7

NON-EMPTY SETS ARE = 2ⁿ - 2

Therefore,

→ (2)⁷ - 2

→ 128 - 2

→ 126 (REQUIRED ANSWER)

Hope it helps you !

shalinikumari0peaks2: this is wrong answer

shalinikumari0peaks2: Answer is 63.
Subset of 6 elements |6| which do not contain 6= 7C6 - 6C5 = 1
Subset of 5 elements |5| which do not contain 5= 7C5 - 6C4 = 6 Subset of 4 elements |4| which do not contain 4= 7C4 - 6C3 = 15 Subset of 3 elements |3| which do not contain 3= 7C3 - 6C2 = 20 Subset of 2 elements |2| which do not contain 2= 7C2 - 6C1 = 15 Subset of 1 element |1| which do not contain 1= 7C1 - 6C0 = 6 Hence, final answer = 1+6+15+20+15+6 = 63

Answered by jefferson7

Of all the nonempty subsets S of { 1, 2, 3, 4, 5, 6, 7}, how many do not contain the number |S|, where |S| denotes the number of elements in S? For example, {3, 4} is one such subset, since it does not contain the number 2.

Step-by-step explanation:

The subset of 5 elements |5| that do not contain 5 = 7C5 - 6C4 = 6

The Subset of 4 elements |4| that do not contain 4 = 7C4 - 6C3 = 15

The Subset of 3 elements |3| that do not contain

3 = 7C3 - 6C2 = 20

The Subset of 2 elements |2| that do not contain 2= 7C2 - 6C1 = 15

The Subset of 1 element |1| that do not contain 1= 7C1 - 6C0 = 6 ∴, we get

= 1 + 6 + 15 + 20 + 15 + 6

= 63

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