Question

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

Answer #1

Answer:)

We see that the truth table for the first statement is given by::

p | q | |

0 | 0 | 1 |

0 | 1 | 0 |

1 |
0 |
1 |

1 | 1 | 1 |

Similarly we see that the table for is :

p | q | |||

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 0 |

1 | 0 | 0 | 1 | 1 |

1 | 0 | 1 | 0 | 1 |

Hence, we see that the truth tables are the same, and hence the two logic statements are equivalent.

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

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 )

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

Construct a truth table to determine whether the following
expression is a tautology, contradiction, or a contingency.
(r ʌ (p
® q)) ↔ (r ʌ ((r
® p) ®
q))
Use the Laws of Logic to prove the following statement:
r ʌ (p
® q) Û r
ʌ ((r ® p)
® q)
[Hint: Start from the RHS, and use substitution, De Morgan,
distributive & idempotent]
Based on (a) and/or (b), can the following statement be
true?
(p ®
q)...

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.

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.

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
}

(1) Determine whether the propositions p → (q ∨ ¬r) and (p ∧ ¬q)
→ ¬r are logically equivalent using either a truth table or laws of
logic.
(2) Let A, B and C be sets. If a is the proposition “x ∈ A”, b
is the proposition “x ∈ B” and
c is the proposition “x ∈ C”, write down a proposition involving a,
b and c that is logically equivalentto“x∈A∪(B−C)”.
(3) Consider the statement ∀x∃y¬P(x,y). Write down a...

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?

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