Let X be a non empty set and S be the collection of all subsets of X. A relation R in S is defined by $R=\{(A,B): A\subseteq B\}$, where $X\subseteq Y$ means $X$ is proper subset of $Y$. Then R is:

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :

Choose the correct answer from the options given below :

Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then :

(A) $f$ is one-one function

(B) $f$ is many to one function

(C) $f$ is bijective function

(D) $f$ is into function

Choose the correct answer from the options given below :

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

Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

Which of the following are correct?

(A) If a ≡ b(mod n), then -a ≡ -b (mod n)

(B) If a + b = c, then a(mod n) + b(mod n) ≡ (a + b + c)(mod n).

(C) If a ≡ b (mod n), then ka ≡ kb(mod n), ∀ k ∈ I.

(D) If a ≡ b (mod n), then (a + k) ≡ (b + k)(mod n), ∀ k ∈ I.

Choose the correct answer from the options given below:

If R be a relation on the set of integers Z, given by R = {(a, b) : (a - b) is a multiple of 3}, then R is: