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The cardinality of the power set of {x: x∈N, x≤10} is ______.
  • a)
    1024
  • b)
    1023
  • c)
    2048
  • d)
    2043
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The cardinality of the power set of {x: x∈N, x≤10} is ______.a...
Given,
Set X = {x: x∈N, x≤10}
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Number of elements of power set of X, P(X) = 210 = 1024
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Most Upvoted Answer
The cardinality of the power set of {x: x∈N, x≤10} is ______.a...
Explanation:
There are 11 elements in the set {x: x∈N, x≤10} which are natural numbers from 1 to 10.

Power Set:
- The power set of a set is the set of all subsets of that set, including the empty set and the set itself.
- The cardinality of a power set of a set with n elements is 2^n.

Calculating the Cardinality of the Power Set:
- Since there are 11 elements in the set, the cardinality of its power set will be 2^11 = 2048.
- Therefore, the cardinality of the power set of {x: x∈N, x≤10} is 2048.
Therefore, the correct answer is option 'A' - 1024.
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The cardinality of the power set of {x: x∈N, x≤10} is ______.a)1024b)1023c)2048d)2043Correct answer is option 'A'. Can you explain this answer?
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