Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) A(x): x is an animal B(x): x is a bear H(x): x is hungry W(x): x is a wolf a. Bears are animals. b. No wolf is a bear. c. Only bears are hungry. d. If all wolves are hungry, so are bears. e. Some animals are hungry bears. f. Bears are hungry but some wolves are not. g. If wolves and bears are hungry, so are all animals. h. Some wolves are hungry but not every animal is hungry.
Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)
A(x): x is an animal
B(x): x is a bear
H(x): x is hungry
W(x): x is a wolf
a. Bears are animals.
b. No wolf is a bear. c. Only bears are hungry.
d. If all wolves are hungry, so are bears.
e. Some animals are hungry bears.
f. Bears are hungry but some wolves are not.
g. If wolves and bears are hungry, so are all animals.
h. Some wolves are hungry but not every animal is hungry.
Explain:
Before we get to the exact solution, let's first define the Quantifier and Predicate.
The predicate is nothing more than the subject's attribute.
Consider the following example:
There is a statement that goes like this:
Y is an even number.
The criteria in this example is "an even integer."
And Y is the subject.
P(Y) on subject Y denotes the predicate.
So, in essence, P is a function.
A quantifier is nothing more than a measure.
Specifically, the quantifier indicates the extent to which the predicate provides the true value across all items.
There are two types of quantifiers:
1. Universal ( for all domains) and
2. Existential ( for some domains ).
For better visualization:
Consider a statement like,
1. Students are honest in this class.
P(x): x is an honest student in this class.
Domain: students in the class.
Then corresponding to the statement predicate logic is:
Given below:
Here, the symbol denotes (for all).
For all x, P(x) is true.
Now let's see the solution to the given questions
for visualization of predicate and quantifier:
The predicate is the following:
Domain: all over the world.
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