Test: Real Analysis - 6 - Mathematics MCQ

Two Unite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are

In the set A = {1,2,3,4, 5}, a relation R is defined by R = {(x , y ) | x, y ∈ A and x < y } . Then,R is

If A and B are two subsets of a set X, then what is A ∩ (A ∪ B)' equal to?

What is the inverse of the function y = 5^{log x}?

For non-empty subsets A, B and C of a set X such that A ∪ B = B ∩ C, which one of the following is the strongest inference that can be derived?

The relation R = {(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} on a set A = { 1 ,2 , 3} is

In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then, the number of student who have passed in Physics only, is

Let R₁ be a relation defined by R₁ = {(a, b ) | a ≥ b, a, b ∈ R}. Then R₁ is

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, and 12 play football and cricket. 8 play all the three games. The total number of members in the three athletic teams is

In a class of 30 pupils, 12 take needle work, 16 take Physics and 18 take History. If all the 30 students take atleast one subject and no one takes all three, then the number of pupils taking 2 subjects is

For a set A, consider the following statements
1. A ∪ P(A) = P(A)
2. {A} ∩ P(A)=A
3. P(A) - {A} = P{A}
where P denotes power set.
Which of the statements given above is/are correct?

The number of elements in the set
{(a, b) : 2a² + 3b² = 35, a b ∈ Z}, where Z is the set of all integer, is

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A x B and B x A are

Assertion (A): y = 2x + 3 is a one-to-one real-valued function.
Reason (R): x₁ ≠ x₂ ==> y₁ ≠ y₂, y₁ = 2 _x1 + 3, y₂ = 2x₂ + 3, for any two real x₁, and x₂

If A, B and C are three finite sets, then what is [(A ∪ B) ∩ C]' equal to

If Q =then 

Consider the following statements
1. φ ∈ {φ}
2. {φ} φ

Which of the statements given above is/are correct?