When “应该” or “该” indicates that it stands to reason for somebody to do something, these two words are interchangeable.
我们应该/该睡觉了。(Wǒmen yīnggāi/gāi shuìjiàole.) We should sleep.
事情那么多，我们应该/该想一想怎么做。(Shìqíng nàme duō, wǒmen yīnggāi/gāi xiǎng yī xiǎng zěnme zuò.) There are so many things, we should think about how to do it.
你不应该/该又迟到。(Nǐ bù yīng gāi/gāi yòu chídào.) You should not be late again.
When introducing the fact, or indicates that one reckons that something is bound to be so, we can only use “应该”.
这台电脑应该是哥哥的，不是弟弟的。(Zhè tái diànnǎo yīnggāi shì gēge de, búshì dìdi de.) This computer should belong to the older brother, not the younger brother.
不要担心，你的考试应该没有问题。(Búyào dānxīn, nǐ de kǎoshì yīnggāi méiyǒu wèntí.) Don’t worry, there should be no problems with your exam.
妈妈喜欢红色，我想她应该喜欢这件衣服。(Māma xǐhuān hóngsè, wǒ xiǎng tā yīnggāi xǐhuān zhè jiàn yīfu.) Mom likes red, I think she should like this dress.
1. When somebody is quite sure about an inference based on certain facts, we can only use “该”.
起晚了，今天又该迟到了。(Qǐ wǎnle, jīntiān yòu gāi chídàole.) Getting up late. I should be late again today.
>>It’s very likely to be late again today.
吃了那么多东西，你该饱了吧？(Chīle nàme duō dōngxi, nǐ gāi bǎole ba?) After eating so many things, you should be full, right?
>>It’s very likely that you are full now.
2. When making an exclamation, we can only use “该”.
该（有/是）+ 多/多么 + Verb/Adjective + 啊
已经出差三个月了，他该多想家啊！(Yǐjīng chūchāi sān gè yuèle, tā gāi duō xiǎng jiā a!) It’s been three months since he had been on a business trip. How much he should be homesick!
我想学习中文，如果我有一个中文老师，该有多好啊！(Wǒ xiǎng xuéxí zhōngwén, rúguǒ wǒ yǒu yīgè zhōngwén lǎoshī, gāi yǒu duō hǎo a!) I want to learn Chinese. If I had a Chinese teacher, it would be wonderful!
3. When indicating it’s somebody’s turn to do something, we can only use “该”.
该 + somebody
我说完了，该你了。(Wǒ shuō wánliǎo, gāi nǐle.) I’m done speaking, it’s your turn now.
这个事情这次是我做的，下次该你做了。(Zhège shìqíng zhè cì shì wǒ zuò de, xià cì gāi nǐ zuòle.) I did the thing this time, and it’s your turn to do it next time.
4. The structure “该 + monosyllabic verb” is often used in oral Chinese. The monosyllabic verb refers to the words such as 打，骂，死 or杀 that means one deserves to be punished due to his or her mistake or some other reasons.
我以前不应该对你那么坏，我该死。(Wǒ yǐqián bù yīng gāi duì nǐ nàme huài, wǒ gāisǐ.) I shouldn’t have treated you so bad before, I deserve to die.
如果你再犯同样的错误，就该打了啊！(Rúguǒ nǐ zàifàn tóngyàng de cuòwù, jiù gāi dǎle a!) If you make the same mistake again, you deserve a hit!
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