Can u(t-2)u(t-a) be simplified in unit step function analysis?

[cahill8]

Homework Statement

I need this to answer a question, its not a homework question itself. Can this be simplified? u(t-2)u(t-a) where u is the unit step function.

Homework Equations

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The Attempt at a Solution

I know the answer is u(t-2) if a <= 2, u(t-a) otherwise. But is there a better way to express this?

 

[Mark44]

Unit step functions are either 0 or 1, depending on the value of t. Look at two cases for a: a < 2 and a > 2, and sketch a graph of u(t - 2) * u(t - a) for each case. (If a = 2, the graph of u(t - 2) * u(t - a) looks exactly like the graph of u(t - 2).)