Question

Fill in the blank with a suitable verb:
You ________ do the washing-up. I've got a washing machine.

• A. should
• B. have to
• C. mustn't
• D. don't have to

Answer 1

The correct option is D don't have to

Answer : D

Let's take a look at the usage of the modal verbs in the options:

• should : It is used for expressing an opinion / advice / expectation / criticism about some past action or it can be used to ask for an advice
• have to : It is used to express an external obligation in positive sentences and removing an external obligation (or necessity) in the negative sentences
• mustn't : It is the contracted form of 'must not'; it is used to talk about things we need to avoid doing; Mustn’t is usually used when the obligation comes from the person who is speaking.
• don't have to : It is the negative form of "have to"; & is used to express that something is not a necessity / obligation; & is used to express absence of an obligation or necessity

Here in the question, we see that the speaker is expressing that as he / she has a washing machine there is no need to do the manual washing-up. So here basically they are eliminating the necessity to do the washing-up.

• "should" is NOT appropriate because it is not used to eliminate a necessity, rather is is used to express an opinion or advice or expectation or criticism.
  
• "have to" is NOT appropriate because it is used to express a necessity or obligation and NOT remove it; also "have to" is not used in construction of negative sentences without the verb being in the negative form
• "mustn't" is NOT appropriate here because it is used to talk about thing that needs to be avoided, here in this case, the third person can still do the washing up despite having a washing machine.
• "don't have to" is the most appropriate verb because it eliminates the necessity, it means that there is no need to do the washing-up because they have a washing machine, but they can do it manually if they'd like to.
  

Therefore from among the options, 'don't have to' is the most suitable verb to complete the sentence.

Thus, the correct complete sentence is:

You DON'T HAVE TO do the washing-up. I've got a washing machine.