This topic involves the issue of "mutual provision". The so-called "mutual offer" means that both parties to the contract send the same offer to each other at the same time. In theory and practice, it is still controversial whether the mutual offer can make the contract established. However, from the perspective of encouraging transactions, most people still believe that mutual offers can make the contract established, provided that the offers are clear and specific and reach both parties.

In this topic, Party A and Party B sent letters with the same contents to each other on the same day (the contents of the letters constitute an offer), and the offer has reached both parties, which is a valid mutual offer and the contract should be established.

2. This expression of intention constitutes an offer.

One of the elements of the establishment of an offer is that the intention is clear and specific. The so-called "clear and specific" means that the expression of intention of an offer should include the contents necessary for the establishment of a contract, generally including price and quantity.

The existing quantity (100 vehicles) and price (1each vehicle in 50 yuan) given by A in this question constitute an offer. Of course, the quantity (100 vehicles) in the meaning expression of this question may be controversial, that is, the unit of measurement of "vehicles", such as whether "vehicles" refer to trucks or carts. However, this kind of dispute can be settled through negotiation between the two parties, and it can also be inferred according to the trading habits and the contents of the contract, which should not prevent the expression of will from forming an offer.

3. The contract is established.

Analysis of the same problem 1 belongs to mutual offer. And Party A has taken further measures to fulfill the contract, that is, "rejecting other customers", so the contract should be judged to be established to protect Party A's trust interests.

4. The invitation letter is: (1) A asks the salesman B: "How much can I sell this fashion?" ; (2) B asked, "How much do you pay?" .

The quotation is: (1) A Answer: "400 yuan, do you want to sell it?" ; (2) B replied: "At least 800 yuan, if it is missing, it will not be sold!" .

Invitation to offer refers to the expression of intention sent by one party to another party to make an offer to the other party, and its content is not required to be specific, as long as it reflects the intention of making an offer to the other party.

An offer refers to a party's expression of intention to conclude a contract with a specific party. Its content requirements are specific and clear, generally including the price and quantity of the contract, and it is necessary to show that the offeror is willing to accept the constraints of the offer.

5. The contract between Party A and Party B is established.

According to the contract law of our country, the contract is established when the acceptance reaches the offeror. In this question, the fax sent by Party A is an offer, and the fax replied by Party B constitutes a promise. When the commitment reaches Party A, the contract is established.

Whether the contract between Party A and Party C is established depends on whether there are other trading habits between Party A and Party C. ..

According to Article 22 of China's Contract Law: "An acceptance is made by notice, except that it can be made through behavior according to trading habits or offers." In this topic, although Party C didn't make a promise through notification, and Party A's offer didn't indicate that it could be made through behavior, if there is a certain trading habit between Party A and Party C (for example, after Party A keeps sending faxes, Party C delivers the goods by itself, and Party C doesn't need to reply to the fax again), then according to this trading habit, Party C's sending cement constitutes a promise and the contract is established. Otherwise the contract is not established.

6. When this contract is established, Party A constitutes a breach of contract.

According to Article 36 of China's Contract Law: "The parties agree to conclude a contract in writing, but if one party has fulfilled its main obligations and the other party accepts it, the contract is established". In this topic, although the two parties have not yet concluded a contract in the form of a contract, both parties have fulfilled their main obligations (delivered 9 tons of goods) and accepted it, and the contract is established. Party A's refusal to continue delivery constitutes a breach of contract.

7. The mortgage contract was established in June 1 year and came into effect in June 15.

According to Article 32 of the Contract Law: "If the parties conclude a contract in the form of a contract, the contract is established when both parties sign or seal it".

According to article 187 of the Property Law, the mortgage of real estate takes effect when the mortgage is registered.

Legally speaking, this topic involves the theoretical problems of real right behavior. The promulgation of China's property law indicates that China has recognized the separation of property right contract and property right act, thus correcting the defects of the previous security law and its judicial interpretation. According to relevant precedents, contract law and property law, the mortgage contract is established at the time of signing and takes effect at the time of registration.