Answer
a. Student Abdallad Hussein does not like Japanese.
b. There exists a student that likes Korean and all students like Mexican
c. There exists a cuisine that Monique Arsenault or Jay Johnson likes.
d. For every two students there exists a cuisine such that if the students arc not the same student, then they do not both like the same cuisine.
e. There exists two students such that for every cuisine, the students both like the cuisine or the students both do not like the cuisine.
f. For every two students there exists a cuisine such that the students both like the cuisine or the students both do not like the cuisine.
Work Step by Step
a. Student Abdallad Hussein does not like Japanese.
T(x,y) means that student x likes cuisine y
$\neg$ means NOT
b. There exists a student that likes Korean and all students like Mexican
T(x,y) means that student x likes cuisine y
$\exists $ means THERE EXISTS, $\land$ means AND, $\forall$ means EVERY
c. There exists a cuisine that Monique Arsenault or Jay Johnson likes.
T(x,y) means that student x likes cuisine y
$\exists$ means THERE EXISTS, $\lor$ means OR
d. For every two students there exists a cuisine such that if the students arc not the same student, then they do not both like the same cuisine.
T(x,y) means that student x likes cuisine y
$\exists$ means THERE EXISTS, $\land$ means AND, $\forall$ means EVERY, $\neg$ means NOT
e. There exists two students such that for every cuisine, the students both like the cuisine or the students both do not like the cuisine.
T(x,y) means that student x likes cuisine y
$\exists$ means THERE EXISTS, $\leftrightarrow$ means IF-AND-ONLY-IF, $\forall$ means EVERY.
f. For every two students there exists a cuisine such that the students both like the cuisine or the students both do not like the cuisine.
T(x,y) means that student x likes cuisine y
$\exists$ means THERE EXISTS, $\leftrightarrow$ means IF-AND-ONLY-IF, $\forall$ means EVERY.
