Given is a relation on bitstrings:
$$R = \{(b,b') | ((b = b') \lor (b = 0b')) \}$$
$0b'$ means the concatenation of $0$ with $b'$.
Is this relation symmetric?
In my opinion it is. If $b = b'$ is true, then $b' = b$ is also true, right? And since it's an OR it doesn't matter that $b = 0b'$ is not the same as $b' = 0b$, right? Because the truth table for OR is:
$$\begin{array} \\1\quad 1 \quad=\quad 1 \\ 1\quad 0\quad =\quad 1 \\ 0\quad 1\quad =\quad 1 \\ 0\quad 0\quad =\quad 0\end{array}$$
But the solution manual says its not symmetric. Could somebody explain that to me please?
Thanks
$\langle 01,1\rangle\in R$, but $\langle 1,01\rangle\notin R$, so it's not symmetric. The or means that you have two cases to deal with, and you do have to deal with both of them.