Question

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)

B(x) is “x is a ball.”

R(x) is “x is round.”

S(x) is “x is a soccer ball.”

1) some balls are round but soccer balls are not

2) if soccer balls are round, then all balls are round

Answer #1

the above are the predicate logics for the above english statements.

In the first statement

Some balls are round shown as

There exists x(b(x)^r(x)) then but soccer balls are not round

Shown as there exists x (s(x) ^r(x)')

-- in the second statement

If the soccer balls are round shown as

Forall x (s(x) -> r(x) then all are round will be represented as

Forall x(b(x) -> r(x)

In the predicate if there is 'some' in the statement max times we use thereexists and ^ symbol to represent in predicate logic

In the statement we encounter 'if then' then we must use -> in the predicate logic.

Using the predicate symbols shown and the appropriate
quantifiers, write each English language statement as a predicate
wff. (The domain is the whole world.)
B(x) is “x is a ball.”
R(x) is “x is round.”
S(x) is “x is a soccer ball.”
All soccer balls are round. ______________________
Some balls are soccer balls.____________________
There exists a ball that is not a soccer
ball._________________
Every ball is round.___________________________

Negate each of the statement below as an English sentence. For
each sentence, introduce predicate and domain and express the
sentence in terms of predicate and quantifiers symbolically, then
negate the sentence symbolically and then as an English
sentence.
(c) For every two integers n and m, if n or m is even then nm is
even.
(d) There is a program that gives the correct answer to every
question that is posed to it.

a) Write equivalent predicate statements for the following
English statement
i. Every teacher loves some painter [2]
ii. Some painter loves some teacher [2]
iii. Every teacher who is also a painter loves Bob [3]
b) If you send me an email, then I will finish my program. If you
do not send me an email, then I will go
to sleep early. Therefore If I go to sleep early. Is this argument
valid [10]

write the following sentences as quantified logical statements, using the universal and existential quantifiers, and defining predicates as needed.
Second, write the negations of each of these statements in the same way.
Finally, choose one of these statements to prove. If it is true, prove it, and if it is false, prove its negation. Your proof need not use symbols, but can be a simple explanation in plain English.
1. If m and n are positive integers and mn is...

1.Write the negation of the following statement in English. Do
not simply add the words “not” or “it is not the case that” or
similar before the existing statement. “Every dog likes
some flavor of Brand XYZ dog food.”
2. Prove that the compound statements are logically equivalent
by using the basic logical equivalences (13 rules). At each step,
state which basic logical equivalence you are using. (p → q) ∧ (¬r
→ q) and (p ∨ ¬r) → q

Language Survey About 42.3% of Californians speak a language
other than English at home. Using your class as the sample, conduct
a hypothesis test to determine if the percent of students at De
Anza College that speak a language other than English at home is
different from 42.3%.
DATA TO USE: 21 out of 34 students in the sample speak a
language other than English at home
A) p-value = ______________ In 1 – 2 complete sentences, explain
what the...

using dr.racket programing language
If we write a function that tests whether a list contains only
strings, odd numbers, or even numbers, you will notice that the
code that iterates through the list stays the same, with the only
change being the predicate function that checks for the desired
list element. If we were to write a new function for each of the
tests listed above, it would be more error-prone and an example of
bad abstraction. We could write...

How would I write this using the correct statistical language.
including symbols?
I chose option 1 for this week’s discussion. I believe the
population mean number of times that adults ate fast food each week
is 2.5. My data is after speaking to with 7 people and found that
they ate fast food 1, 4, 0, 2, 4, 0 and 3 times last week. I choose
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For table shown in figure 1 construct (a) a Boolean expression
having the given table as its truth table and (b) a circuit having
the given table as its input/output table. (10 points) Figure 1:
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figure 2 and show that they are logically equivalent when regarded
as statement forms.(16 points) Figure 2: Circuits 7. Let R(m, n) be
the predicate “If m is a factor of n 2 then...

Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions: f, g, h, etc. But remember a function is a special
kind of relation so it might turn out that a Relation, R, is a
function, too.
Relations
To understand the symbolism better, let’s say the domain of a
relation, R, is A = { a, b , c} and the Codomain is B = {
1,2,3,4}.
Here is the relation: a R 1, ...

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