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.
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?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?
If A = { x : x is a multiple of 3} and B = (x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?
Consider the following statements in respect of sets \(A\) and \(B\):
I. If \(x \in A\) and \(A \in B\), then \(x \in B\).
II. If \(A \subset B\) and \(x \notin B\), then \(x \notin A\).
Which of the statements given above 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?
If A is an open set and B is a closed set, then B - A is
If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be
A set containing n elements, has exactly ..... subsets.
If P, Q and R are three sets, then which of the following is correct?
Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, 12 play football and cricket and 8 play all the three games. The total number of members in the three athletic teams is: