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I am quite new to Mathematica and have an issue regarding which statement. 

cut[x_, y_] := which[x>y, doFunctionX[], y>x, doFunctionY[]]
cut/@{X,Y}]

I wish to display only the true case. However, I am unable to find an operation to do it.

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    $\begingroup$ NOt really sure what you're trying to do with the last line, since X and Y are not numbers (and it should be cut[X, Y] anyway). But, if you change which to Which (all built-in functions in Mathematica are capitalized), your code should be fine. When you change that, cut[5, 3] evaluates to doFunctionX[]. $\endgroup$ – march Nov 1 at 15:35
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    $\begingroup$ Here is a good post with common pitfalls for new users. I anchored it to your issue (Mathematica is case sensitive and the built-in system functions always start with a capital letter): mathematica.stackexchange.com/questions/18393/… $\endgroup$ – Arnoud Buzing Nov 1 at 15:52
  • $\begingroup$ You may also want to consider handling the case when x == y. $\endgroup$ – Rohit Namjoshi Nov 1 at 17:54
  • $\begingroup$ Thank you. The issue was due to not capitalizing the first letter. $\endgroup$ – Siddeshwar Raghavan Nov 2 at 16:36
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In Mathematica you can do this with function name overloading. Like so:

cut[x_, y_] /; x > y := doFunctionX[]
cut[x_, y_] /; x < y := doFunctionY[]

where the Condition (/;) operator enforces the conditions you want to place on the arguments.

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