Question 1 :
Let $L$ denote the set of all straight lines in a plane, Let a relation $R$ be defined by $lRm$, iff $l$ is perpendicular to $m$ for all $l \in L$. Then, $R$ is
Question 2 :
Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $aRb$, if $a$ is congruent to $b$ for all $a,b\in T$. Then, $R$ is
Question 3 :
Let N denote the set of all natural numbers and R a relation on $N\times N$. Which of the following is an equivalence relation?
Question 4 :
Let $A=\left\{ 2,3,4,5,....,17,18 \right\} $. Let $\simeq $ be the equivalence relation on $A\times A$, cartesian product of $A$ with itself, defined by $(a,b)\simeq (c,d)$, iff $ad=bc$. The the number of ordered pairs of the equivalence class of $(3,2)$ is
Question 6 :
Assertion: $ \displaystyle f:R \rightarrow \left [0,\frac {\pi}{2} \right )$ defined by $ \displaystyle f(x)=\tan^{-1}(x^{2}+x+a)$ is onto for all $ a \in \left ( -\infty ,\dfrac{1}{4} \right )$
Reason: For onto function codomain of $f=$ Range of $f$.
Question 7 :
The relation 'is a factor of' on the set of natural numbers is not___________
Question 8 :
In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.<br/>It is sufficient, if $R$
Question 9 :
Write the properties that the relation "is greter that" satisfies in the set of all positive integers
Question 11 :
Let $f:{x, y, z}\rightarrow (a, b, c)$ be a one-one function. It is known that only one of the following statements is true:(i) $f(x)\neq b$<br/>(ii)$f(y)=b$<br/>(iii)$f(z)\neq  a$
Question 12 :
Let $f:\{x, y , z\} \rightarrow \{1, 2, 3\}$ be a one-one mapping such that only one of the following three statements and remaining two are false : $f(x) \neq 2, f(y) =2, f(z) \neq 1$, then
