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If I pass a signal with DC component through a Low Pass Filter will the output be without the DC component?

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DC = 0 Hz and will not be affected by an LPF. An HPF will remove DC. – Paul R Dec 9 '12 at 7:40
@ape : Did you mix up low pass and high pass? – hotpaw2 Dec 10 '12 at 19:26
Yes I did. My book was wrong and it made sense for the output to be rid of the DC component and they used an LPF where as they should have used an HPF. Thanks! – ape Dec 10 '12 at 20:47

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In most mathematical treatments of DSP, a "DC" signal acts like a frequency component with a frequency and phase of zero (0 Hz).

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