Let A = {-2, -1, 0, 1, 2, 3}. Let R be a rela | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given set $A = \{-2, -1, 0, 1, 2, 3\}$.Relation $R$ is defined as $x R y \iff y = \max \{x, 1\}$.Calculating elements of $R$:For $x = -2, y = \max

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) Given set $A = \{-2, -1, 0, 1, 2, 3\}$.Relation $R$ is defined as $x R y \iff y = \max \{x, 1\}$.Calculating elements of $R$:For $x = -2, y = \max \{-2, 1\} = 1 \implies (-2, 1) \in R$.For $x = -1, y = \max \{-1, 1\} = 1 \implies (-1, 1) \in R$.For $x = 0, y = \max \{0, 1\} = 1 \implies (0, 1) \in R$.For $x = 1, y = \max \{1, 1\} = 1 \implies (1, 1) \in R$.For $x = 2, y = \max \{2, 1\} = 2 \implies (2, 2) \in R$.For $x = 3, y = \max \{3, 1\} = 3 \implies (3, 3) \in R$.So,$R = \{(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 2), (3, 3)\}$.Thus,$l = 6$.For $R$ to be reflexive,we need $(x, x) \in R$ for all $x \in A$. Currently,$R$ contains $(1, 1), (2, 2), (3, 3)$. We need to add $(-2, -2), (-1, -1), (0, 0)$. So,$m = 3$.For $R$ to be symmetric,if $(x, y) \in R$,then $(y, x) \in R$. The pairs in $R$ are $(-2, 1), (-1, 1), (0, 1), (1, 1), (2, 2), (3, 3)$.Symmetry requires $(1, -2), (1, -1), (1, 0)$ to be added. So,$n = 3$.Therefore,$l + m + n = 6 + 3 + 3 = 12$.

Similar Questions

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$

Let $A = \{1, 2, 3\}$. Show that the number of relations on $A$ containing $(1, 2)$ and $(2, 3)$ which are reflexive and transitive but not symmetric is $3$. (Note: The original prompt claimed $4$,but the correct count for this specific set is $3$).

For any two real numbers $a$ and $b$,we define $a R b$ if and only if $\sin ^{2} a+\cos ^{2} b=1$. The relation $R$ is

The relation $R$ is defined on the set $N$ by $R = \{(x, y) | x, y \in N, 2x + y = 41\}$. Then $R$ is:

Relation $S = \{(3,3), (4,4)\}$ on set $A = \{3, 4, 5\}$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module