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The number of elements in the power set of the set {{a, b}, c} is
- a)8
- b)4
- c)3
- d)7
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of elements in the power set of the set {{a, b}, c} isa)8b)...
We can simply solve this problem by using the following mathematical process.
A power set is defined as the set or group of all subsets for any given set, including the empty set. A set that has 'n' elements has 2n subsets in all.
The power set is denoted by the notation P(S) and the number of elements of the power set is given by 2n.
In the given set, the number of elements is 2
Therefore, in the power set, the number of elements will be
Hence, The number of elements in the power set of the set {{a,b},c} is 4.
Most Upvoted Answer
The number of elements in the power set of the set {{a, b}, c} isa)8b)...
A={{a,b},c}
Let 'N' be the no. of elements in set A i.e. N=2
Then, No. of elements in the power set of A = 2^N = 2^2 = 4 Eelements are {{},{{a,b}},{c},{{a,b},c}}
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Community Answer
The number of elements in the power set of the set {{a, b}, c} isa)8b)...
Solution:
The power set of a set is the set of all subsets of that set, including the empty set and the set itself.
The given set is {{a, b}, c}.
To find the power set, we need to consider all possible combinations of elements.
Step 1: Find all possible subsets of the set {a, b}
- The subsets of {a, b} are { }, {a}, {b}, {a, b}
Step 2: Add c to each of the above subsets
- { } U {c} = {c}
- {a} U {c} = {a, c}
- {b} U {c} = {b, c}
- {a, b} U {c} = {a, b, c}
Therefore, the power set of the set {{a, b}, c} is { { }, {c}, {a}, {b}, {a, c}, {b, c}, {a, b}, {a, b, c} }.
Hence, the number of elements in the power set is 4.
Therefore, the correct answer is option B.
The power set of a set is the set of all subsets of that set, including the empty set and the set itself.
The given set is {{a, b}, c}.
To find the power set, we need to consider all possible combinations of elements.
Step 1: Find all possible subsets of the set {a, b}
- The subsets of {a, b} are { }, {a}, {b}, {a, b}
Step 2: Add c to each of the above subsets
- { } U {c} = {c}
- {a} U {c} = {a, c}
- {b} U {c} = {b, c}
- {a, b} U {c} = {a, b, c}
Therefore, the power set of the set {{a, b}, c} is { { }, {c}, {a}, {b}, {a, c}, {b, c}, {a, b}, {a, b, c} }.
Hence, the number of elements in the power set is 4.
Therefore, the correct answer is option B.
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The number of elements in the power set of the set {{a, b}, c} isa)8b)4c)3d)7Correct answer is option 'B'. Can you explain this answer?
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