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1. verb Literally, to remove something by applying a sweeping stroke to it or the surface it's on, typically with one's hand. In this usage, a noun can be used between "brush" and "off" or after "off." Be sure to brush off that chair before you sit down. I stood up and brushed the crumbs off my shirt.
2. verb To casually, unexpectedly, or brusquely dismiss or ignore someone or something. In this usage, a noun can be used between "brush" and "off" or after "off." You can't just brush off the students' questions—they deserve answers. I haven't heard back from that company, so I guess they're brushing my complaint off.
3. verb To deflect or ignore something in order to remain unaffected by it. In this usage, a noun or pronoun is typically used between "brush" and "off." If you're going to write for a major publication, you need to be able to brush off criticism. So you made an error—just brush it off and try to do better next inning.
4. noun The act of casually, unexpectedly, or brusquely dismissing or ignoring someone or something. In this usage, the phrase is usually hyphenated. Be honest and tell John that you're not interested in dating anymore—don't just give him the brush-off. I haven't heard back from that company, so I guess my complaint is getting the brush-off.
Fig. rejection; being cast aside and ignored. (*Typically: get ~; give someone ~.) Don't talk to Tom. He'll just give you the brush-off. I went up to her and asked for a date, but I got the brush-off.