MCQ_SINGLE

Let $S = {1, 2, 3, … , 100}$. The number of non-empty subsets A of S such that the product of elements in A is even is :

MCQ_SINGLE

Let $R$ be the set of real numbers. Statement I: $A = \{(x, y) \in R \times R: y - x \text{ is an integer }\}$ is an equivalence relation on $R$. Statement II: $B = \{(x,y) \in R \times R: x = \alpha y \text{ for some rational number } \alpha\}$ is an equivalence relation on $R$.

MCQ_SINGLE

Let $S = {1, 2, 3, …, 10}$. Suppose $M$ is the set of all the subsets of $S$, then the relation $R = {(A, B) : A ∩ B ≠ 𝜙; A, B ∈ M}$ is :

MCQ_SINGLE

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

MCQ_SINGLE

Two sets A and B are as under : A = {$(a, b) ∈ R × R : |a - 5| < 1$ and $|b - 5| < 1$}; B = {$(a, b) ∈ R × R : 4(a - 6)^2 + 9(b - 5)^2 ≤ 36$}; Then

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