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.
Sets
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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.
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