In mathbb{R}, a relation p is defined as foll | vedclass

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(C) The relation is defined as $a^2-4ab+3b^2=0$. $1$. Reflexivity: For any $a \in \mathbb{R}$, we check if $a \ p \ a$. Substituting $b=a$, we get $a^

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$p$ is only reflexive

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(C) The relation is defined as $a^2-4ab+3b^2=0$. $1$. Reflexivity: For any $a \in \mathbb{R}$, we check if $a \ p \ a$. Substituting $b=a$, we get $a^2-4a(a)+3a^2 = a^2-4a^2+3a^2 = 0$. Since $0=0$, the relation is reflexive. $2$. Symmetry: Check if $a \ p \ b \implies b \ p \ a$. If $a^2-4ab+3b^2=0$, then $(a-b)(a-3b)=0$, so $a=b$ or $a=3b$. If $a=3b$, then $b=a/3$. For symmetry, we need $b^2-4ba+3a^2=0$. Substituting $a=3b$, we get $b^2-4b(3b)+3(3b)^2 = b^2-12b^2+27b^2 = 16b^2 
eq 0$ (unless $b=0$). Thus, it is not symmetric. $3$. Transitivity: Check if $a \ p \ b$ and $b \ p \ c \implies a \ p \ c$. If $a=3b$ and $b=3c$, then $a=9c$. For $a \ p \ c$, we need $a^2-4ac+3c^2=0$. Substituting $a=9c$, we get $(9c)^2-4(9c)c+3c^2 = 81c^2-36c^2+3c^2 = 48c^2 
eq 0$. Thus, it is not transitive. Therefore, the relation is only reflexive.

In $\mathbb{R}$, a relation $p$ is defined as follows: $\forall a, b \in \mathbb{R}$, $a \ p \ b$ holds if $a^2-4ab+3b^2=0$. Then:

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