Chapter 1.5, Problem 7E

LetT(x,y) mean that studentxlikes cuisiney, where the d

omain forxconsists of all students at your school and the domain foryconsists of all cuisines. Express each of these statements by a simple English sentence.

a) $\neg T\left(\text{Abdallah}\text{Hussein,}\text{Japanese}\right)$

b) $\exists xTx\left(x,\text{Korean}\right)\wedge \forall xT\left(x,\text{Mexican}\right)$

c) $\exists y\left(T\left(\text{Monique}\text{Arsenault},y\right)\vee T\left(\text{Jay}\text{Johnson},y\right)\right)$

d) $\forall x\forall z\exists y\left(\left(x\ne z\right)\to \neg \left(T\left(x,y\right)\wedge T\left(z,y\right)\right)\right)$

e) $\exists x\exists z\exists y\left(T\left(x,y\right)\leftrightarrow T\left(z,y\right)\right)$

f) $\forall x\forall z\forall y\left(T\left(x,y\right)\leftrightarrow T\left(z,y\right)\right)$