Book page $489$ Problem $7$

Let isFatherOf $(x,y)$ be $"x$ is the father of $y"$ where the domain is the set of all people now living or who have lived. Find the truth value for each of the following wffs$.$

a$.$ AAxEEy isFatherOf $(x,y).$

b$.$ AAyEEx isFatherOf $(x,y).$

c$.$ EExAAy isFatherOf $(x,y).$

d$.$ EEyAAx isFatherOf $(x,y).$

e$.$ EExEEy isFatherOf $(x,y).$

f$.$ EEyEEx isFatherOf $(x,y).$

g$.$ AAxAAy isFatherOf $(x,y).$

h$.$ AAyAAx isFatherOf $(x,y).$

Consider the following five predicates

$,p(x)-x$ is a person"

$,c(x)-"x$ likes chocolate ice cream"

$v(x)-"x$ likes vanilla ice cream"

$s(x)-"x$ likes strawberry ice cream"

$,eq(x,y)-x$ equals $y^{\text{'}\text{'}}$

Write "Every person who likes both vanilla and chocolate ice cream also likes strawberry ice cream." as a quantified expression using these predicates.

$9.$ Consider the following three predicates

$d(x)-"x$ is a day"

$,s(x)-"x$ is sunny"

$r(x)-"x$ is rainy"

$,eq(x,y)-x$ equals $y^{\text{'}\text{'}}$

and the two constants

$,m-$"Monday"

$,t-$ "Tuesday"

Write $"$It is rainy on a day other than Monday and Tuesday." as a quantified expression using these predicates and constants as needed. $($Hint: There are more than two named days, but do not introduce any new constants or predicates.$)$ Computer foundation