State the truth value of each of the predicate will below as

State the truth value of each of the predicate will below as well as give as English translation if P(x); x is positive N(x): x is negative G(x, y): x > y S(x, y): x

Solution

(a) English Translation - There exists atleast one x for all y such that if y is negative then z>=y

this statements is true as z domain is all Intger so all positive numbers are greate than negative y.

(b) English Translation - There exists atleast one x in the intersection of domain of non positve integer(compliment on P(x) ) and non negative integer .

this statements is true as 0 will be in the intersection of domain of non positve integer and non negative integer .

(c)

for all x and y ,if x<= y then x is negative

this statement is wrong as lets take x =3 and y=9 so x<y but x is not negative ,so its contadiction. hence,this statement is wrong