On April 20, 2017, John and Mary sign the following contract: - If it rains on M

Question

On April 20, 2017, John and Mary sign the following contract:

- If it rains on May 1, 2017, then John must give Mary a check for $10,000 on May 2, 2017
- If John gives Mary a check for $10,000 on May 2, 2017, Mary must mow the lawn on May 3, 2017.

What truly happened those days is the following:
- it did not rain on May 1, 2017
- John gave Mary a check for $10,000 on May 2, 2017
- Mary mowed the lawn on May 3, 2017.

Part a: Write a propositional-logic statement to express the contract. Make sure that, for each symbol that you use, you clearly define what that symbol stands for.


Part a: Write a logical statement to express what truly happened. When possible, use the same symbols as in question 4a. If you need to define any new symbols, clearly define what those new symbols stand for.


Part a: Was the contract violated or not, Justify your answer

Explanation / Answer

R(z) --Rained on day z (domain for z is day)
G(x,y,z) - x gives cheque of 10000 to y on day z//domain of x and y are people
M(x,z) -- x mow the lawn on day z

The contract

R(May 1,2017)-->G(John,Mary,May 2,2017)
G(John,Mary,May 2,2017)->M(Mary,May 3,2017)

Actual happened

Not R(May 1,2017)
G(John,Mary,May 2,2017)
M(Mary,May 3,2017)

The contract did not get violated. The statement says if it rains then John must
give the cheque to Mary.So if it does not rain it is upto John whether he gives
cheque to Mary or not. But once cheque has been given every thing has happened
as per the contract.

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