We want to look at the Dehn twists $t_a$, $t_b$ and $t_c$ about the curves $a$, $b$ and $c$ in $D_4$ (a $4$-punctured disc). Are either of the following statements true in the mapping class group of $D_4$ rel boundary, MCG($D_4$, $\partial D_4$ ):$t_b\in<t_a,t_c>$ or $t_a\in <t_b, t_c>$?

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