Question

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.

Answer #1

Use a truth table to determine whether the following argument is
valid.
p
→q ∨ ∼r
q →
p ∧ r
∴ p →r

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

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

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

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.

Prove: (p ∧ ¬r → q) and p → (q ∨ r) are biconditional using
natural deduction NOT TRUTH TABLE

Let p, q, and r represent the following simple statements.
p:
It is snowing outside
q:
It is cold
r:
It is cloudy.
Write the following compound statement in its symbolic form.
If
it is snowing outside
then
it is cold
or
it is not cloudy

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
}

[16pt] Which of the following formulas are semantically
equivalent to p → (q ∨ r): For each
formula from the following (denoted by
X) that is equivalent to p → (q
∨ r), prove the validity of X
« p → (q ∨
r) using natural deduction. For
each formula that is not
equivalent to p → (q ∨ r), draw its truth table
and clearly mark the entries that result in the
inequivalence. Assume the binding priority used in...

Given: (P & ~ R) > (~R & Q), Q> ~P Derive: P >
R. use propositional logic and natural derivation rules.

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