2. (10 pts) Suppose A and B are the statements: A: Alex traveled to Spain. B: Bill traveled to Spain.
a. Translate “Alex and Bill both traveled to Spain” into symbols.
b. Translate “Alex or Bill traveled to Spain” into symbols.
c. Translate “Bill traveled to Spain, but Alex did not” into symbols.
d. Translate “If Alex traveled to Spain, then Bill did not” into symbols.
e. Translate “A∨B” into English.
f. Translate “¬A∨¬B” into English.
g. Translate “¬(A∧B)->B” into English.
h. If ¬A∨¬B is true, is it possible that Bill traveled to Spain? Explain.
i. Suppose you know that if Alex traveled to Spain, Bill did too. What can you conclude if you know that:
i. Bill traveled to Spain.
ii. Bill did not travel to Spain.