Translating If and And Statements Coursework Assignment (Coursework Sample)

Translating If and And Statements
Students Name:
Institution:
Statements
1 If it rains, the pitch will get slippery, then the match will be cancelled.
2 Since the storm started, there has been tree falls and foods in most regions
Logically; statement 1 can be divided in to three parts in the translation key.
Statement 1
If it rains, the pitch will get slippery, then the match will be cancelled can be interpreted to mean that: it is true that raining will lead to the match being postponed because the pitch will be slippery.
If we divide it into x – if it rains, y – the pitch will get slippery, and z – then the match will be cancelled. Then we can say that x results to z, which means that, z is true on condition that x is true
[(x → z) ˄ x] → z
However, the above statement symbolize the syllogism law of logic reason which states: if x → y and y → z, then x → z is also true.
Noted as:
[(x → y) ˄ (y → z)] → (x → z)
Statement 1 is an “if” statement because it has a conclusion that follows a hypothesis (Hopcroft, Motwani & Ullman 2006). In this case, the part “if” it rains is a hypothesis and the conclusions are two: the pitch will get slippery; the match will be cancelled. x → y → z .
Statement 2
Since the storm started, there has been tree falls and foods in most regions can be interpreted to mean: x - since the storm started, there has been tree falls in some regions; and y - since the storm started, there has been floods in most regions.
Logically, the and in this statement is used as a conjunction to join sentences x and y which are due to one c...