$4.$ Generate grammar rules for a language that allows strings to contain an arbitrary number of paired letters $"$XY$".$ Complete the tasks listed below.

Some valid examples include:

$\backslash (\backslash$mathrm$\{$XY$\},\backslash$mathrm$\{$XYXY$\},\backslash$mathrm$\{$XYXYXYXY$\}\backslash )$

Some invalid examples include:

$\backslash (\backslash$mathrm$\{$X$\},\backslash$mathrm$\{$XYY$\},\backslash$mathrm$\{$YX$\},\backslash$mathrm$\{$XXXYYY$\}\backslash )$

Tasks:

$4.$a$.$ Write the grammar rules to ensure any strings have an arbitrary number of $\backslash (\backslash$mathbf$\{$X Y$\}\backslash )$ pairs.

$4.$b$.$ Using the grammar rules from part $(4.$a$),$ write a leftmost derivation to arrive at the sentential form XYXYXY$.$

$4.$c$.$ Draw the parse tree representing the sentential form XYXYXY$.$