Q$6.$ Show that a lattice $($A$,)($A$,\backslash$leq$)($A$,)$ is distributive if and only if$,$ for any a$,$b$,$c in Aa$,$ b$,$ c $\backslash$in Aa$,$b$,$c in A$,$

$($a$$b$)($b$$c$)($c$$a$)=($a$$b$)($b$$c$)($c$$a$).($a $\backslash$land b$)\backslash$lor $($b $\backslash$land c$)\backslash$lor $($c $\backslash$land a$)=($a $\backslash$lor b$)\backslash$land $($b $\backslash$lor c$)\backslash$land $($c $\backslash$lor a$).($a$$b$)($b$$c$)($c$$a$)=($a$$b$)($b$$c$)($c$$a$).$

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