Consider the following statements:
1. The set of irrational numbers between \(\sqrt2\) and \(\sqrt5\) is infinite.
2. The set of all odd integers less than100 is finite.
Which statement(s) is/are correct?
1 only
Only 1 is true. Every nonempty real interval contains infinitely many irrational numbers. Odd integers below 100 include all negative odd integers, so that set is also infinite; statement 2 is false.
If A = {λ, {λ, μ}}, then the power set of A is
If A, B and C are subsets of a given set, then which one of the following relations is not correct?
Let X be a non-empty set and let A, B, C be subsets of X, consider the following statements:
1) A ⊂ C ⇒ (A ∩ B) ⊂ (C ∩ B), (A ∪ B) ⊂ (C ∪ B)
2) (A ∩ B) ⊂ (C ∪ B) for all sets B ⇒ A ⊂ C
3) (A ∪ B) ⊂ (C ∪ B) for all sets B ⇒ A ⊂ C
Which of the above statements is/are correct?A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?
Let S = {2, 4, 6, 8, ______ 20}.
What is the maximum number of subsets does S have?Consider the following statements for the two non-empty sets A and B:
1) (A ∩ B) ∪ (A ∩ B̅) ∪ (A̅ ∩ B) = A ∪ B
2) (A ∪ (A̅ ∩ B̅)) = A ∪ B
Which of the above statements is/are correct?Consider the following statements:
1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets.
2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets.
Which of the above statements is/are correct?
Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?
If S = {x : x 2+ 1 = 0, x is real}, then S is
If A = {λ, {λ, μ}}, then the power set of A is
If A = {x, y, z}, then the number of subsets in powerset of A is