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The total number of subsets of the set {1,3,5,7} is A.8 B.10 C.12 D.16

The total number of subsets of the set {1,3,5,7}
is
A.8
B.10
C.12
D.16

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Hint: Number of subsets of a set is given by the formula =2n , where n is the number of elements in the set. In this question we are given a set, so first we will find the number of subset in the set and then by using the formula 2n we will determine the number of the subset that the given set can have. Complete step-by-step answer: Given the set S={1,3,5,7} Now from the given set we can see there are 4 numbers of elements are there hence we can write n=4 Now as we know the number of subset in the set can be determined by the formula 2n , hence by substituting the values we can write 2n Subset=2n=24=16 Hence we can say the total number of subsets of the set {1,3,5,7} is =16 To check There are total of 16 subsets so now we will enlist them to verify Write all the single element s as each element of a set is also its subset, we get {1},{3},{5},{7} Now enlist subset with two elements {1,3},{1,5},{1,7},{3,5},{3,7},{5,7} Now enlist subset with three elements {1,3,5},{1,3,7},{3,5,7},{1,5,7} Now since there are total of 4 element s so this will be counted as one subset {1,3,5,7} Now we will list {ϕ} since an empty set is also a subset. Hence we can say the number of subsets of the set {1,3,5,7} is =16 So, the correct answer is “16”. Note: The position of element in a set does not matter, if the element of a set is represented as {a,b} or {b,a} then the set is same. A subset of a set is the collection of all elements that are part of another set. We can see if the element of set A is {p,q,r} and of set B is {p,q} then set B is the subset of set A.

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