Tessellate S.T.E.M.S (2019) - Computer Science - College - Set 2 - Subjective Problem 1

Suppose $\rightarrow$ is a binary relation on $A$ , i.e, $\rightarrow \; \subseteq A \times A$ .

The reflexive closure of $\rightarrow$ is the smallest relation that contains $\rightarrow$ but also satisfies $a \rightarrow a$ for every $a \in A$ .
The symmetric closure of $\rightarrow$ is the smallest relation that contains $\rightarrow$ but also satisfies $a \rightarrow b$ whenever $b \rightarrow a$ hold for some $a, b \in A$ .
The transitive closure of $\rightarrow$ is the smallest relation that containts $rightarrow$ but also satisfies $a \rightarrow c$ whenever $a \rightarrow b$ and $b \rightarrow c$ hold for some $a, b, c \in A$ .

Prove or disprove: The Symmetric closure of the reflexive closure of the transitive closure of any relation $\rightarrow$ is an equivalence relation.

This problem is a part of Tessellate S.T.E.M.S (2019)

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$