Mathematics
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.
Answer
Given set A = {1, {Φ}}
Proper subset of A = Φ, {1}, {{Φ}}
So, assertion (A) is true.
The only subset of empty set is itself, so we can say that empty set does not have a proper subset.
So, reason (R) is true but reason does not explains assertion.
Hence, option 2 is the correct option.
Related Questions
Let M = {factors of 12} and N = {factors of 24} then {24} is equal to :
M ∪ N
M ∩ N
M - N
N - M
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.
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.
Assertion (A) : Let A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 5, 7, 9} then A ∩ B ⊆ A and A ∩ B ⊆ B, always true for every pair of two sets.
Reason (R) : For any sets A and B, we have A ∩ B ⊆ A and A ∩ B ⊆ 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.