Set Definition by Notation: If solutions of $x_j=1$ and $y_j=0$, j is element of set A. Is it correct to use:$A= \{ \forall j:x_j=1, y_j=0 \}$?

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I would like to specify a set as follows:

If solutions of $x_j=1$ and $y_j=0$, j is element of set A. Is it correct to use the following notation?

$$A= \{ \forall j:x_j=1, y_j=0 \}$$