Question

Express each of these statements using predicates and quantifiers.

Answer 1

Answer:

a) $\forall \ x \ ( f(x) \lor g(x) \ \rightarrow e(x))$

b) $\forall \ x \ ( m(x) \land c(x, 3.5)) \lor ( \neg m(x) \land c(x,3.5)) \ \rightarrow q(x))$

c) $M \rightarrow ((H(60) \lor (H(45) \land W)) \land \forall \ y \ G(B,y)$

d) $\exists x (C(x) \land A(x))$

Step-by-step explanation:

A Predicate is a sentence that contains a finite number of variables and becomes  a statement when specific values are substituted for the variables.

The domain of  a predicate variable is the set of all values that may be substituted in place of the  variable.

Quantifiers are words that refer to quantities such as ”some” or ”all” and tell for  how many elements a given predicate is true.

a)

$f(x) : x$ is flying more than 25000 miles in a year

$g(x) : x$ takes more than 25 flights during that year

$e (x) : x$ qualifies as an elite flyer

b)

$m(x):x$ is a man

$c(x, y) : x$ has the change if previous time is less than y

$q (x)$ : qualifies for the marathon

c)

$M:$ received Master's degree

$H(x):$ took $x$ hours for the course

$W:$ wrote thesis

$G (x, y) :$ graded $x$ or higher in course $y$

d)

$c(x) : x$ taken more than 21 credit hours in a semester

$A(x) : x$ has received all A