Question

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

Answer #1

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...

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

Construct an indirect truth table for this argument.
∼A • ∼(R ∨ Q) / B ≡
∼Q // B ⊃ J
From your indirect truth table what can you conclude?
The argument is valid and the value of the letter R is True.
The argument is valid and the value of the letter R is
False.
The argument is invalid and the value of the letter R is
True.
The argument is invalid and the value of the letter R is
False.

Write a C++ program to generate
all the truth tables needed for ( p
˄ q) ˅ (¬ p ˅ (
p ˄ ¬ q )). You need to submit
your source code and a screen shot for the output

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

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 )

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.

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

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

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