Question

are
they logically equivalent (show how) truth table or in word::

a) p —> ( q —> r ) and ( p -> q) —> r

b) p^ (q v r ) and ( p ^ q) v ( p ^ r )

Answer #1

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.

1. Construct a truth table for: (¬p ∨ (p → ¬q)) → (¬p ∨ ¬q)
2. Give a proof using logical equivalences that
(p → q) ∨ (q →
r) and (p → r)
are not logically equivalent.
3.Show using a truth table that (p →
q) and (¬q →
¬p) are logically equivalent.
4. Use the rules of inference to prove that the premise
p ∧ (p
→ ¬q) implies
the conclusion ¬q. Number each
step and give the...

Let P and Q be statements:
(a) Use truth tables to show that ∼ (P or Q) = (∼ P) and (∼
Q).
(b) Show that ∼ (P and Q) is logically equivalent to (∼ P) or (∼
Q).
(c) Summarize (in words) what we have learned from parts a and
b.

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

Are the statement forms P∨((Q∧R)∨ S) and ¬((¬ P)∧(¬(Q∧ R)∧ (¬
S))) logically equivalent? I found that they were not logically
equivalent but wanted to check. Also, does the negation outside the
parenthesis on the second statement form cancel out with the
negation in front of P and in front of (Q∧ R)∧ (¬ S)) ?

Show the following are not logically equivalent: ∀xP (x) ∨
∀xQ(x) and ∀x(P (x) ∨ Q(x)).

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

Use two truth tables to show that the pair of compound
statements are equivalent.
p ∨ (q ∧ ~p); p ∨
q
p
q
p
∨
(q
∧
~p)
T
T
?
?
?
?
?
T
F
?
?
?
?
?
F
T
?
?
?
?
?
F
F
?
?
?
?
?
p
∨
q
T
?
T
T
?
F
F
?
T
F
?
F

Write a C++ program to construct the truth table of P ||
!(Q && R)

[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...

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