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If you wish to use copyright material which consists of a short quotation from a published work and you have acknowledged and referenced it adequately then it will probably not be necessary to seek permission from the copyright holder.
However if the re-use is not covered by a licence or an exception in copyright law you will need to obtain permission from the rights holder. It is important that you keep a copy of any letters or emails you receive from rights holders. If you do not get permission or do not receive a response you cannot use the material.