सत्, चित् and आनन्द are स्वरूपलक्षण, meaning the defining attributes or the very nature, of ब्रह्मात्मा । This is in contrast to the तटस्थलक्षण which is an incidental attribute of ब्रह्म। The stock example for the latter is the "house with the crow sitting on the roof". The house is known by the the crow sitting on top of the roof at the moment when it is shown, but the crow is obviously neither the part of the house nor the nature of the house. An example for the former is the sweetness of sugar. There is no sugar without sweetness, so it is the defining attribute or the very स्वरूप of sugar. So that becomes the स्वरूपलक्षण of sugar. In the case of ब्रह्मात्मा, सत्, चित् and आनन्द define the nature. What is to be noted that when a particular thing is said to be a defining attribute of something, its impact is two fold-- for one, that attribute is not seen elsewhere and for another, wherever that attribute is seen, it is due to that very thing! Sugar is the only sweet thing and any sweetness experienced anywhere is due to sugar alone. This would mean that existence, consciousness and bliss belong only to ब्रह्मात्मा and the corollary of that statement is that wherever any of existence, consciousness and bliss is seen, it is all due to ब्रह्मात्मा alone. These three different words characteristic of ब्रह्मात्मा each have a different sense in regular usage, how then can they be defining the same ब्रह्म which is आत्मा? This is discussed further.
For these three defining words to be in समानाधिकरण्य (grammatical apposition) and represent the same वस्तु ब्रह्मात्मा, they have to have an overlap over one another in one way or the other. This is clear when you analyse the other two from the point of any one. Lets start with सत् which is easily explained so. Both, consciousness and bliss to really mean anything concrete, more so, to be used as a defining attribute, they need to be existent first! So consciousness is not an absence but existent consciousness. So too, bliss is existential bliss. Next, consciousness. For one to know that one is existing, one doesn't need anything or anyone else. I have to be conscious, that is self-conscious, to know that I exist. And I know I exist. So mine is a conscious existence. Similarly, I know when happy or waking up from deepest of sleep, that I slept happily. That knowledge is a recollection of sleep-happiness. Only that can go in memory and recollected which is collected first. So happiness was collected during sleep and recollected on waking up. And collecting experience of happiness is possible only for a conscious entity. So the happiness was conscious happiness. That lands us on bliss. This is the most difficult to see, but no one can deny the fear of anything, particularly, death. The very idea that I may not exist some day is scary. Also such a fear brings sadness, that is, it takes away my happiness. That which when lost makes one sad has to be of the nature of happiness. So existing is blissfully existing, not otherwise. Lack of knowledge of something also results in fear or sadness, so knowledge also is blissful, making it blissful consciousness.
This is how all three attributes are related and talk of one's own real nature which is only but one ब्रह्मात्मा। Wherever anything is seen to be existent, conscious or source of happiness, it is all owed to the self alone, nay, it is self alone.
ॐ तत् सत्।