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Multiplication of Piecewise functions

I have two separate Piecewise functions wit the same domain ranges.  Is it possible to get a third PWF  that is the product of the first two?
POSTED BY: Jose Calderon
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p1 = Piecewise[{{1, x < 1}}, 2];
p2 = Piecewise[{{2, x > 2}}, 1];
p3 = PiecewiseExpand[p1*p2]
POSTED BY: Frank Kampas
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