Question

Discret Math MATH/CSCI2112

(3) (a) Write the following premises and the conclusion as logical statements and prove the conclusion correct: (use the symbols in brackets).

If the flight is late, I will spend the night in Toronto. If I miss my flight I will spend the night in Winnipeg. Either my flight is not late, or I did not miss my flight from Winnipeg, but not both. Therefore either I will spend the night in Toronto, or I will spend the night in Winnipeg. (L, T, M, W)

(b) If the conclusion is changed to: "Either I will spend the night in Toronto or I will spend the night in Winnipeg, but not both" Is the conclusion still correct?

Answer 1

if the flight is late then I will spend the night in Toronto.

if I miss my flight then I will spend the night at Winnipeg.

Either my ight is not late, or I did not miss my ight from Winnipeg, but not both.

so if my flight is not late , then I missed my flight[since both can not happen],hence i will spend the night at WInnipeg.

and if i did not miss my flight, then my flight is late[since both can not happen].hence i will spend the night at Toronto.

hence the conclusion that Therefore either I will spend the night in Toronto, or I will spend the night in Winnipeg is true.

b) now the conslusion is changed to "Either I will spend the night in Toronto or I will spend the night in Winnipeg, but not both"

this means that it will not happen that I will spend the night in toronto AND I will spend the night in Winnipeg.

so 2 things may happen

i) I will spend the night in Toronto and I will not spend the night in WInnipeg

ii) I will not spend the night in Toronto and I will spend the night in Winnipeg.

from i) the conclusion is my flight is late and I did not miss my flight

from ii) the conclusion is that my flight is not late and I missed my flight.

combining both we get that Either my flight is not late, or I did not miss my flight from Winnipeg, but not both

hence the conclusion is still correct