儿 [Er] child
儿子 [Érzi] son
女儿 [Nǚ'ér] daughter
So, why is 儿 in different positions in each word but they are both valid?
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This is an interesting question, because it allows us to look at how words are formed in modern Chinese.
Both 兒 and 子 meant "child" or "son" in ancient Chinese. 兒 was more specific, while 子 had a variety of other uses, like "master" (as in 孔子 - master Kong/Confucius). When 子 meant child, it was somewhat inclusive of female children, although it can also refer to males only, as in the sentence
无子,有女二人 [he had] no sons, but two daughters.
兒 can sometimes be used for "children" in general, as in the modern 兒童, but in ancient Chinese, it tended to be male-specific. The Qin dynasty proto-dictionary 倉頡篇 Cangjiepian gives the definition:
男曰儿,女曰婴 male [young children] are called 兒, female [ones] are called 嬰.
When 兒 refers to the child of someone, it means son.
女 means daughter, but has always also meant "woman" or "female (human)".
As the pronunciation of the Chinese language changed over the centuries, many one-syllable words became homophones. In order to clarify which word they meant, people formed two-syllable words that were less likely to be confused. Three very common ways to do this are:
褲子 (pants)all mean the exact same thing with or without the 子
It’s easy to see how 兒子 follows all three of these rules. I suspect it was formed by the third rule, because the 子 is pronounced in the fifth / neutral tone, which suggests it does not carry the meaning of the word.
So why 女兒 instead of 女子? Firstly, 女子 can mean daughter or "female child". But it can also refer to "women" in general. So 女兒 is more specific.
And why not 兒女? The word "daughter" would not be formed this way, because 女 is more specific than 兒, which can be gender-neutral. Therefore, 兒女 reads as "sons and daughters", which is indeed what it means.
儿(=兒) is optional. 子 already means "son", and 女 (used to) mean "daughter". E.g. 育有一子一女 means "feed one son and one daughter".
In Old Chinese, most words were monosyllabic. While in modern Chinese, most words consist of two or more characters, so 儿 is added. Why is 儿 in different positions in 儿子 (son), 女儿 (daughter)? Mainly because other candidate two character words have had meanings.
儿女 means "sons and daughters" or "(young) people".
男儿 is the same meaning as "man" in phrases "be a man", "man enough".
In fact, 女儿 also has other meanings. It could mean "unmarried girls" or "(young) women".
I see the above answer can not say wrong, but I feel a little strange. "儿" You can understand the children of parents. 儿子的"子" Represents men: the child is a boy. 女儿的"女" represents a woman: the child is a girl. In Chinese, parents said a son is "儿子" or "小儿" (xiao er), and a girl is "妮儿" (nin er).
The above mentioned is limited to "儿子", "女儿". If you have to connect to (桌子) the table, this is without any meaning. Do you understand?