Answer Happy

Provide a truth table that includes all five statement
forms and their truth values.
Short answer and definition questions
Directions: Answer each question as
completely as possible, complete sentences may be necessary.
2) A conditional/hypothetical statement is false when the
_____________ is true and the ________________ is false.
3) Give the definition of validity.
4) A self-contradictory statement is a statement whose truth
values are always ______________.
5) A disjunction asserts what, in other words, when is the
statement true?
6) When considering the truth values of two logically equivalent
statements, why can they be substituted for each other?
7-8) Provide a truth table for the following statements, if A is
false, B is false and C is true.
~[~(A • B) ⊃C] v
B
~{[(C • ~A) v B] ⊃
[~(C ⊃A) ⊃ B]}
9) Provide a truth table for the following statement.
(4 pts.)
(A ⊃ B) ≡ (~A v B)
10) Is the statement in question 9 a tautology,
self-contradictory, or contingent statement? Depending on
your previous answer, does this relationship exhibit a rule of
equivalence? If so, what is its name?
(4 pts.)
11-12) Determine whether the following arguments are valid or
invalid using a short-form truth table.
5 pts. each
A ⊃ (A v
B)
(A
⊃ B) • (C ⊃D)
~A ~B
v ~D
~(A v
B)
~A v
~C
Symbolic Translation:
Translate the following sentences into symbolic notation.
4 pts. each
13) Mary will run only if Harry will not stop following her.
14) Either you are happy and the test is going well, or you are
not happy and the test is not going well.
15) It is not the case that if you are good at symbolizing then
you are good at proofs, but if you are good at proofs then you are
good at symbolizing.
16) Give two logically equivalent statements in symbolic
notation, not using tautology or double
negation, for the following statement:
(5 pts.)
(~R • S) v T
17) Give two logically equivalent statements in symbolic
notation, not using tautology or double
negation, for the following statement:
(5 pts.)
(~A ⊃ B) ⊃ ~C
18) Give the name of the rule of inference used for each line in
the proof, including the lines used to make the inference.
(10 pts.)
1) (R v S) ⊃
~T
1) B ⊃C
2) S
2)
D v B
3) U v
T 3) D ⊃E
U
E v C
4) R v S
_______________
4) (D ⊃E) • (B ⊃C) ________________
5)
~T 5)
E v
C
________________
6) U
_______________
19) Name the rule for the following arguments and equivalent
statements.
(2 pts each)
B ⊃
C
~(B • C) ≡ (~B v ~C)
C ⊃ E
B ⊃ E
(W • Y) ⊃ (X ⊃
Z)
{[(A v B) • C] ⊃ D} ≡ {~D ⊃ ~[(A v
B) • C]}
~(X ⊃ Z)
~(W • Y)
20) Provide proofs for the following arguments.
(5 pts possible)
B ⊃
C
(A ⊃ B) v D
~C A
~B v (D •
E)
~D
• E
B
21) Write a three premise (using at least two compound
statements) valid argument, translate in to symbolic notation and
show its validity in a truth table.
(5 pts)
22) Give the definition of an argument in the logical sense.
(pass or fail exam)
Bonus
Symbolize the following two statements:
(4 pts possible)
You are finished with the exam, unless you are a slow
writer.
Neither is it difficult, nor is it easy to symbolize
statements.