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Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to
[JEE 2010]
- a)25
- b)34
- c)42
- d)41
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint ...
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Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint ...
Explanation:
Given:
S = {1, 2, 3, 4}
Finding the number of unordered pairs of disjoint subsets:
To find the number of unordered pairs of disjoint subsets of S, we first need to find the total number of subsets of S.
Finding the total number of subsets of S:
The number of subsets of a set with n elements is given by 2^n.
For S = {1, 2, 3, 4}, n = 4
Therefore, the total number of subsets of S = 2^4 = 16
Finding the number of unordered pairs of disjoint subsets:
For any given set, the number of ways to form two disjoint subsets is 3^n, where n is the number of elements in the set.
So, for S = {1, 2, 3, 4}, the number of unordered pairs of disjoint subsets = 3^4 = 81
However, this includes ordered pairs, so we need to subtract the number of ordered pairs.
The number of ordered pairs can be found by multiplying the number of ways to choose a subset from 16 subsets for the first subset and 15 subsets for the second subset.
So, the number of ordered pairs = 16 * 15 = 240
Therefore, the total number of unordered pairs of disjoint subsets = 81 - 240 = 41
Therefore, the correct answer is option 'D' - 41.
Given:
S = {1, 2, 3, 4}
Finding the number of unordered pairs of disjoint subsets:
To find the number of unordered pairs of disjoint subsets of S, we first need to find the total number of subsets of S.
Finding the total number of subsets of S:
The number of subsets of a set with n elements is given by 2^n.
For S = {1, 2, 3, 4}, n = 4
Therefore, the total number of subsets of S = 2^4 = 16
Finding the number of unordered pairs of disjoint subsets:
For any given set, the number of ways to form two disjoint subsets is 3^n, where n is the number of elements in the set.
So, for S = {1, 2, 3, 4}, the number of unordered pairs of disjoint subsets = 3^4 = 81
However, this includes ordered pairs, so we need to subtract the number of ordered pairs.
The number of ordered pairs can be found by multiplying the number of ways to choose a subset from 16 subsets for the first subset and 15 subsets for the second subset.
So, the number of ordered pairs = 16 * 15 = 240
Therefore, the total number of unordered pairs of disjoint subsets = 81 - 240 = 41
Therefore, the correct answer is option 'D' - 41.
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Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to [JEE 2010]a)25b)34c)42d)41Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to [JEE 2010]a)25b)34c)42d)41Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to [JEE 2010]a)25b)34c)42d)41Correct answer is option 'D'. Can you explain this answer?.
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