Question

Use a truth table to determine whether the following argument is valid.

*p*
→*q* ∨ ∼*r*

*q* →
*p* ∧ *r*

∴ *p* →*r*

Answer #1

Use
a truth table to determine whether the two statements are
equivalent.
~p->~q, q->p
Construct a truth table for ~p->~q
Construct a truth table for q->p

a.
Translate the argument into sympolic form.
b. Use a truth table to determine whether the argument is
valid or invalid.
If there is an ice storm, the roads are dangerous.
There is an ice storm
The roads ate dangerous
b. Is the given argument valid or invalid?

Use a truth table to determine if the following is a
logical equivalence: ( q → ( ¬
q → ( p ∧ r ) ) ) ≡ ( ¬ p ∨ ¬ r )

Indicate whether the argument form is valid
(V), or invalid (I). Show your work.
~p ∨ (~q ∨ r)
~p ⊃ r
∴ q ∨ r
Indicate whether the argument form is valid
(V) or invalid (I). Show your work.
~p ≡ q
p ⊃ q
∴ ~p ● q

Create truth tables to prove whether each of the following is
valid or invalid.
You can use Excel
1. (3 points)
P v R
~R
.: ~P
2. (4 points)
(P & Q) => ~R
R
.: ~(P & Q)
3. (8 points)
(P v Q) <=> (R & S)
R
S
.: P v Q

1.)
The definition of valid argument is as follows.
Whenever the premises are all true, the conclusion is true as
well.
Create an equivalent definition that is the
contrapositive of the definition above.
2.)
Show that the following argument is valid without using
a truth table. Instead, argue that the argument fulfills the
equivalent definition for valid argument that you created in number
(1)
p→¬q
r→(p∧q)
¬r

Use a truth table or the short-cut method to determine if the
following set of propositional forms is
consistent: { ¬ p ∨ ¬ q ∨
¬ r, q ∨ ¬ r ∨ s, p ∨ r ∨ ¬ s, ¬ q ∨ r ∨ ¬ s, p ∧ q ∧ ¬ r ∧ s
}

For three statements P, Q and R, use truth tables to verify the
following.
(a) (P ⇒ Q) ∧ (P ⇒ R) ≡ P ⇒ (Q ∧ R).
(c) (P ⇒ Q) ∨ (P ⇒ R) ≡ P ⇒ (Q ∨ R).
(e) (P ⇒ Q) ∧ (Q ⇒ R) ≡ P ⇒ R.

use truth tables to determine whether or not the following
arguments are valid:
a) if jones is convicted then he will go to prison. Jones will
be convicted only if Smith testifies against him. Therefore , Jones
won't go to prison unless smith testifies against him.
b) either the Democrats or the Republicans will have a
majority in the Senate. but not both. Having a Democratic majority
is a necessary condition for the bill to pass. Therefore, if the
republicans...

1) Show that ¬p → (q → r) and q → (p ∨ r) are logically
equivalent. No truth table and please state what law you're using.
Also, please write neat and clear. Thanks
2) .Show that (p ∨ q) ∧ (¬p ∨ r) → (q ∨ r) is a tautology. No
truth table and please state what law you're using. Also, please
write neat and clear.

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