My professor gave us a study guide a few days ago and the answers to it today. I did the study guide and thought I did it all right, but saw some of my answers were not the same as his. I tried emailing him, but he hasn't responded yet so I wanted to reach out here.
The instructions were: Translate each of the following sentences into the Blocks language of Tarski’s World.
It is not the case that c is larger than d, but d is larger than e.
- My answer: $\sim$Larger(c,d) $\wedge$ Larger(d,e)
- His answer: $\sim$Larger(c,e) $\wedge$ Larger(c,e)
I thought my answer was right because I used all the constants in the right order and because but means "and".
It is not the case that a is either to the left of or in front of b.
- My answer was: $\sim$(LeftOf(a,b) $\wedge$ FrontOf(a,b))
- His answer: $\sim$(LeftOf(a,b) $\vee$ FrontOf(a,b))
I thought my answer was right because "Not the case" means negation, "either" clues us into the use of parenthesis, but then I get confused after that. I thought "or" meant v so since ~ is in front of the whole argument we use ^ due to DeMorgan's Rule. Or since the word "either" is in the sentence does that "or" actually mean "and"?
Either both a and e are tetrahedron or neither a nor f is.
- My answer: (Tet(a) $\wedge$ Tet(e)) $\vee$ $\sim$(Tet(a) $\vee$ Tet(f))
- His answer: (Tet(a) $\wedge$ Tet(a)) $\vee$ $\sim$(Tet(a) $\wedge$ Tet(f))
- I think he meant: (Tet(a) $\wedge$ Tet(e)) $\vee$ $\sim$(Tet(a) $\wedge$ Tet(f))
I thought my answer was right because DeMorgan's rule made $\sim$(Tet(a) $\vee$ Tet(f)) mean a is not a tetrahedron and f is not a tetrahedron because I thought neither...nor. meant "and". Or am I missing something in how the sentence was written?
In all three cases I agree with your answers, rather than the professor's. In fact, it looks like your professor put this study guide together rather hurriedly, given some of the obvious mistakes in not using the right constant symbols.