Use the method of truth table expansion to determine whether or not the sentence below is a theorem of quantified logic. The # indicates a biconditional, usually indicated by a double arrow.

(EX)(Y)FXY#(Y)(EX)FXY

Solution Preview

I am assuming that (EX) is the existential quantifier "There exists an x such that..." and that (Y) is the universal quantifer "For all Y the following holds..."

The trick is to pick a small finite universe, such as one with two elements A and B.

Then the expresion (EX)FX expands to FA v FB ( here I use "v" for logical or")
That is, for a unverse of two elements, if there exists an x such that the predicate F about x is true, this can only be the case if the predicate F is true for either the first element A or the second element B. Another way of saying this is that applying the existential quantifier to an expression is the same as applying to the "or" operation between each possible value of the ...

Solution Summary

The validity of a symbolic logic expression is investigated. A method of truth table expansions are used.

For each of problems,
? Write a symbolic version of the given statement
? Construct a negation of the symbolic statement
? Translate the symbolic negation into good, lucid English.
Problem A: "All the routers in our facility support both hard-wired and wireless Internet connections."
Problem B: "Each of our salespersons h

1) Determine the truth value for each simple statement. Then use these truth values to determine the truth value of the compound statement
17 ≥ 17 and −3 > −2
2) Write the statement in symbolic form.
Let
p: The tent is pitched.
q: The bonfire is burning.
The tent is pitched and the bonfire is burning
3) D

SymbolicLogic
PART 1
1. Write two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives. (If your computer does not have all the symbols needed, use some other symbol you do have access to and

The sentence below is a theorem of predicate logic. Show that it is by deriving it from the null set of premises. If any "individual" in the domain has a property, then every individual has it. I need help explaining this and with the derivation.
(EX)(FX --->(Y)FY)

Transcribe the English argument below into an appropriate logical language adequate to determine it to be valid. Also, please provide a derivation of the conclusion from the premises within the same logical system (by which you transcribed it). *this seems to be predicate logic and probably requires universal and existential q

Translate the following argument in symbolic form and determine whether it's logically correct by constructing a truth table.
If affirmative action policies are adopted, then minorities will be hired. If minorities get hired, then discrimination will be addressed. Therefore, if affirmative action policies are adopted, then d

1. Write the statement in symbolic form and construct a truth table.
The zoo is open, but it is not a nice day.
2. Use DeMorgan's laws to determine whether the two statements are equivalent.
? (p V ?q), ?p ^ q
3. Determine the truth value of a statement.
15-7=22 or 4+8=13, and 9-8=1

Please show all steps and explain as necessary so that I can follow. I'm not sure if the omission of the word "hen" is significant to the argument. Is that why the argument is not correct?
Determine if this argument is correct, using symboliclogic and a truth table. If it is not correct, explain what is wrong with the argume

1. Determine whether ~ [~ (p V ~q) <=> p V ~q. Explain the method(s) you used to determine your answer.
2. Translate the following argument into symbolic form. Determine whether the argument is valid or invalid. You may compare the form of the argument to one of the standard forms or use a truth table.
If Spielberg is t