Are both B and Y ions required to determine the sequence of a protein by mass spectrometry?
In an MS/MS spectrum, difference between the successive peaks of a b or y ion series allows one to determine the amino acids making the series/peptide. Either one of them should be enough to give you the sequence. However, an MS/MS spectrum obtained from the mass spec instrument doesnt tell fragment types. Therefore it takes some expertise and tricks to spot y or b ion series. For example: if you are analysing a sample digested by trypsin, your C-term residue will either be K or R. So you can look for a Y1 ion if there is 147 indicating K or 175 indicating R. Also, Y ions tend to be highest intensity peaks in a spectrum. For more helpful tips on this there is an excellent tutorial : 
http://www.ionsource.com/tutorial/DeNovo/DeNovoTOC.htm.

Also, in practice you seldom get all of the b or y ion peaks and there are often missing peaks. For this reason it is useful to have both b and y ions series so that gaps in one can be filled by the other. This is not only useful when you are dealing with denovo sequencing but also in a more typical shotgun proteomics experiment. In a typical shotgun proteomics experiment one searches their mass spec data with peptide search engines. These are software which use a protein sequence database which is in silico digested, based on the specificity of the protease used in the experiment, and from the resulting peptide sequences search engines make a library of predicted MS/MS spectra (this is done by fragmenting along the peptide backbone and listing all possible b and y ions). Then these predicted spectra are matched with the observed spectra to predict the peptide sequences that could result in the observed spectra. Again, not all of the peaks present in a predicted spectra will be found in an observed spectra. So it is best to have ions from both b and y ion series. More ions matched between the observed and predicted spectra, better is the score and confidence in identification.