Class JEE Mathematics Sets, Relations, and Functions Q #1035
KNOWLEDGE BASED
APPLY
4 Marks 2023 JEE Main 2023 (Online) 31st January Evening Shift MCQ SINGLE
Among the relations
$S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$ and $T = {(a, b) : a, b \in R, a^2 - b^2 \in Z}$,
(A) $S$ is transitive but $T$ is not
(B) both $S$ and $T$ are symmetric
(C) neither $S$ nor $T$ is transitive
(D) $T$ is symmetric but $S$ is not
Prev Next
Correct Answer: D
Explanation
For relation $T$: if $(a, b) \in T$, then $a^2 - b^2 = I$ where $I \in Z$.
Then, $(b, a)$ on relation $T$ means $b^2 - a^2 = -I$.
Since $-I \in Z$, $T$ is symmetric.
For relation $S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$, $2 + \frac{a}{b} > 0 \implies \frac{a}{b} > -2$.
If $(b, a) \in S$ then $2 + \frac{b}{a}$ is not necessarily positive. Therefore, $S$ is not symmetric.

More from this Chapter

NUMERICAL
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\ge$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is _______________.
MCQ_SINGLE
Let a relation $R$ on $N \times N$ be defined as: $(x_1, y_1) R (x_2, y_2)$ if and only if $x_1 \le x_2$ or $y_1 \le y_2$. Consider the two statements: (I) $R$ is reflexive but not symmetric. (II) $R$ is transitive Then which one of the following is true?
NUMERICAL
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is _________.
MCQ_SINGLE
Let $R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}$ be a relation on the set $A = \{3, 6, 9, 12\}$. The relation is :
NUMERICAL
Let $A=\{1,2,3,4\}$ and $\mathrm{R}$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $\mathrm{R}$ is ____________.
View All Questions