Mathematics
Let M = {factors of 12} and N = {factors of 24} then {24} is equal to :
M ∪ N
M ∩ N
M - N
N - M
Sets
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Answer
M = {factors of 12}
Factors of 12 = 1, 2, 3, 4, 6, 12
M = {1, 2, 3, 4, 6, 12}
N = {factors of 24}
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
N = {1, 2, 3, 4, 6, 8, 12, 24}
M ∪ N = {1, 2, 3, 4, 6, 12} ∪ {1, 2, 3, 4, 6, 8, 12, 24}
= {1, 2, 3, 4, 6, 8, 12, 24}
M ∩ N = {1, 2, 3, 4, 6, 12, 24} ∩ {1, 2, 3, 4, 6, 8, 12, 24}
= {1, 2, 3, 4, 6, 12}
M - N = {1, 2, 3, 4, 6, 12} - {1, 2, 3, 4, 6, 8, 12, 24}
= {}
N - M = {1, 2, 3, 4, 6, 8, 12, 24} - {1, 2, 3, 4, 6, 12}
= {8, 24}
Hence, none of the given options are correct.
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A set has 5 elements, then number of its subsets is :
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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 = {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.