Let T be the set of all triangles in a Euclid | vedclass

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

Question

(D) To determine the nature of the relation $R$ defined by similarity $(a \sim b)$: $1$. Reflexive: Every triangle $a$ is similar to itself $(a \sim a

Vedclass · Accepted Answer

An equivalence relation

Vedclass · Answer

(D) To determine the nature of the relation $R$ defined by similarity $(a \sim b)$: $1$. Reflexive: Every triangle $a$ is similar to itself $(a \sim a)$. Thus,$aRa$ holds. So,$R$ is reflexive. $2$. Symmetric: If triangle $a$ is similar to triangle $b$ $(a \sim b)$,then triangle $b$ is also similar to triangle $a$ $(b \sim a)$. Thus,$aRb \implies bRa$. So,$R$ is symmetric. $3$. Transitive: If triangle $a$ is similar to triangle $b$ $(a \sim b)$ and triangle $b$ is similar to triangle $c$ $(b \sim c)$,then triangle $a$ is similar to triangle $c$ $(a \sim c)$. Thus,$aRb$ and $bRc \implies aRc$. So,$R$ is transitive. Since the relation $R$ is reflexive,symmetric,and transitive,it is an equivalence relation.

Let $T$ be the set of all triangles in a Euclidean plane and a relation $R$ on $T$ is defined as $aRb$ if and only if $a \sim b$ (where $a \sim b$ denotes that triangle $a$ is similar to triangle $b$) for all $a, b \in T$. Then $R$ is:

Similar Questions

Let $R$ be a transitive relation on a set $A$ and $I$ be the identity relation on $A$. Then:

Let $N$ be the set of natural numbers and a relation $R$ on $N$ be defined by $R = \{(x, y) \in N \times N : x^{3}-3x^{2}y-xy^{2}+3y^{3}=0\}$. Then the relation $R$ is:

Let $N$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_1 = \{(x,y) \in N \times N : 2x + y = 10\}$ and $R_2 = \{(x,y) \in N \times N : x + 2y = 10\}$. Then

Let $A = \{2, 3, 6, 8, 9, 11\}$ and $B = \{1, 4, 5, 10, 15\}$. Let $R$ be a relation on $A \times B$ defined by $(a, b) R (c, d)$ if and only if $3ad - 7bc$ is an even integer. Then the relation $R$ is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module