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which one of following can't be no of elements in power set of any finite set(a) 26 (b)32 (c)8 (d)16
Most Upvoted Answer
which one of following can't be no of elements in power set of any fin...
Explanation:
The power set of any finite set is the set of all subsets including the empty set and the set itself. The number of elements in the power set is given by 2^n, where n is the number of elements in the original set.
(a) 26: This cannot be the number of elements in the power set of any finite set because 2^n is always a power of 2, and 26 is not a power of 2.
(b) 32: This can be the number of elements in the power set of a set with 5 elements, since 2^5 = 32.
(c) 8: This can be the number of elements in the power set of a set with 3 elements, since 2^3 = 8.
(d) 16: This can be the number of elements in the power set of a set with 4 elements, since 2^4 = 16.
Therefore, the answer is (a) 26, as it is not a possible number of elements in the power set of any finite set.
The power set of any finite set is the set of all subsets including the empty set and the set itself. The number of elements in the power set is given by 2^n, where n is the number of elements in the original set.
(a) 26: This cannot be the number of elements in the power set of any finite set because 2^n is always a power of 2, and 26 is not a power of 2.
(b) 32: This can be the number of elements in the power set of a set with 5 elements, since 2^5 = 32.
(c) 8: This can be the number of elements in the power set of a set with 3 elements, since 2^3 = 8.
(d) 16: This can be the number of elements in the power set of a set with 4 elements, since 2^4 = 16.
Therefore, the answer is (a) 26, as it is not a possible number of elements in the power set of any finite set.
Community Answer
which one of following can't be no of elements in power set of any fin...
26 is the correct option
because we know that no of subsets=2^n
Now for 1 element 2^1=2
For 2 elements 2^2=4
For 3 elements 2^3=8
For 4 elements 2^4=16
For 5 elements 2^5=32
But 26 cant be no. of elements in power set
because we know that no of subsets=2^n
Now for 1 element 2^1=2
For 2 elements 2^2=4
For 3 elements 2^3=8
For 4 elements 2^4=16
For 5 elements 2^5=32
But 26 cant be no. of elements in power set
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which one of following can't be no of elements in power set of any finite set(a) 26 (b)32 (c)8 (d)16
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