Question 1 :
Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is
Question 2 :
The relation $R$ defined on set $A = \left \{x :|x| < 3, x\epsilon I\right \}$ by $R = \left \{(x, y) : y = |x|\right \}$ is
Question 3 :
A set $A$ has $3$ elements and another set $B$ has $6$ elements. Then
Question 4 :
A relation $R$ is defined on the set $Z$ of integers as follows: R=$(x,y)$ $\displaystyle \in {R}:x^{2}+y^{2}= 25$. Express $R$ and $\displaystyle R^{-1}$ as the sets of ordered pairs and hence find their respective domains.
Question 5 :
A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :$(x,y)\in\;R\; \rightarrow x$ is relatively prime to y. Then, domain of R is
Question 6 :
If the relation $R:A\rightarrow B$, where $A=\left \{1,2,3\right \}$ and $B=\left \{1,3,5\right \}$ is defined by $R=\left \{(x,y):x < y, x\in A, y\in B\right \}$, then
Question 9 :
If {tex} f: R \rightarrow S , {/tex} defined by {tex} f ( x ) = \sin x - \sqrt { 3 } \cos x + 1 {/tex} is onto, then the interval of {tex} S {/tex} is
Question 10 :
In a class of 50 students, 18 take music, 26 take art and 2 take both art and music. How many students in the class are not enrolled in either music or art?
Question 11 :
Let $n(A) = n$. Then the number of all relations on $A$ is
Question 12 :
If {tex} f : [ 0 , \infty ) \rightarrow [ 0 , \infty ) {/tex} and {tex} f ( x ) = \frac { x } { 1 + x } , {/tex} then {tex} f {/tex} is
Question 13 :
The function {tex} f : R \rightarrow R {/tex} defined by {tex} f ( x ) = ( x - 1 ) ( x - 2 ) ( x - 3 ) {/tex} is
Question 14 :
Let $A$ and $B$ be two sets containing four and two elements respectively.Then the number of subset of the set $A \times B$, each having at least three elements is <br>
Question 15 :
The relation R define on the set of natural numbers as {(a, b) : a differs from b by 3} is given.
