Mathematics
Statement 1: The number of subsets of {{1, {0}}, 2} is 8.
Statement 2: A set containing 'n' elements has 2n - 1 proper subsets.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Given set : {{1, {0}}, 2}
The set A = {{1, {0}}, 2} has two elements : {1, {0}} and 2.
Thus, n = 2.
The number of subsets of a set with n elements = 2n = 22 = 4.
Thus, statement 1 is false.
We know that,
The total number of proper subsets of a set with n elements is 2n - 1.
Thus, statement 2 is true.
Hence, option 4 is the correct option.
Related Questions
A set has 5 elements, then number of its subsets is :
25
52
25 - 1
2 x 5
Let M = {factors of 12} and N = {factors of 24} then {24} is equal to :
M ∪ N
M ∩ N
M - N
N - M
Assertion (A) : Let A = {1, {Φ}}, then each of Φ, {1}, {{Φ}} is a proper subset of A.
Reason (R) : The empty set has no proper subset.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : Let A = {factors of 12} and B = {factors of 16}. Then B - A = {8, 16}
Reason (R) : B - A = {x | x ∈ A, but x ∉ B}.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.