i have to do an exercise for the university , i did that but i'm so sure that is right so:
• “The tumor is benign” A • “The tumor is metastatic” B • “The tumor has a good prognosis” C Express the following statements in Propositional Logic: 1. The tumor has a good prognosis only if it is either benign or not metastatic. 2. A tumor cannot be benign and metastatic at the same time. 3. If the tumor is not metastatic, it is either benign or has a good prognosis.
To my opinion the result should be:
1.A XOR ¬B ---> C
2.¬A AND B
3.¬B--->A XOR C
i read in Internet that i can convert either..or.. with the logical operation XOR but i'm not sure that my result is right because as second question is asked which of these formulas are equivalent, but i tried to do the true table and no one has the same result. Can everyone help me please?