PHIL 240 FINAL EXAM QUESTIONS
AND CORRECT ANSWERS
(VERIFIED ANSWERS) A GRADE
~(∀x)(Px ⊃ ~Qx) : : _________ (C.Q.N.) - correct answer-
~(∀x)(Px ⊃~ Qx) : : (∃x)(Px • Qx)
[~E ≡ I]
~(∀x)(Px ⊃ Qx) : : _________ (C.Q.N.) - correct answer-
~(∀x)(Px ⊃ Qx) : : (∃x)(Px • ~Qx)
[~A ≡ O]
~(∀x)(Px) : : _________ (Q.N.) - correct answer- ~(∀x)(Px)
: : (∃x)~(Px)
~(∀x)~(Px) : : _________ (Q.N.) - correct answer-
~(∀x)~(Px) : : (∃x)(Px)
~(∃x)(Px • ~Qx) : : _________ (C.Q.N.) - correct answer-
~(∃x)(Px • ~Qx) : : (∀x)(Px ⊃ Qx)
[~O ≡ A]
,~(∃x)(Px • Qx) : : _________ (C.Q.N.) - correct answer-
~(∃x)(Px • Qx) : : (∀x)(Px ⊃ ~Qx)
[~I ≡ E]
~(∃x)(Px) : : _________ (Q.N.) - correct answer- ~(∃x)(Ax)
: : (∀x)~(Px)
~(∃x)~(Px) : : _________ (Q.N.) - correct answer-
~(∃x)~(Ax) : : (∀x)(Px)
★ Conditional Exchange (Description) ★ - correct answer-
For a conditional, we can translate it to a disjunction with the
denial of the antecedent. This works because of Modus Ponens
and Modus Tollens. If P then Q is true under the following
circumstances: 1) P and Q are both true, 2) Q is true, 3) P and Q
are both false. if P then Q is false only when P is true but Q is
false. This is the same for the disjunction (~P v Q).
1. (~P v Q) when P and Q are true = (~P v Q) = true
2. (~P v Q) when only Q is true = (P v Q) = true
3. (~P v Q) when both are false = (P v ~Q) = true
, 4. (~P v Q) when P is true but Q is false = (~P v ~Q) = false
One disjunct MUST be true for the disjunction to be true.
1. Either the visiting team does not score, or I will eat my hat is
equivalent to if the visiting team scores, then I will eat my hat.
★ Conditional Exchange (Symbols) ★ - correct answer-
(P ⊃ Q) : : (~P v Q)
★ DeMorgan's (Description) ★ - correct answer- For
conjunctions and disjunctions, you can distribute a negation by
negating every part of the statement, including the operator.
Negating a disjunction makes it a conjunction.
Negating a conjunction makes it a disjunction.
The logic of this is as follows:
1a. (not P) and (not Q) is equivalent to not (P or Q)
1b. (not P) or (not Q) is equivalent to not (P and Q)
AND CORRECT ANSWERS
(VERIFIED ANSWERS) A GRADE
~(∀x)(Px ⊃ ~Qx) : : _________ (C.Q.N.) - correct answer-
~(∀x)(Px ⊃~ Qx) : : (∃x)(Px • Qx)
[~E ≡ I]
~(∀x)(Px ⊃ Qx) : : _________ (C.Q.N.) - correct answer-
~(∀x)(Px ⊃ Qx) : : (∃x)(Px • ~Qx)
[~A ≡ O]
~(∀x)(Px) : : _________ (Q.N.) - correct answer- ~(∀x)(Px)
: : (∃x)~(Px)
~(∀x)~(Px) : : _________ (Q.N.) - correct answer-
~(∀x)~(Px) : : (∃x)(Px)
~(∃x)(Px • ~Qx) : : _________ (C.Q.N.) - correct answer-
~(∃x)(Px • ~Qx) : : (∀x)(Px ⊃ Qx)
[~O ≡ A]
,~(∃x)(Px • Qx) : : _________ (C.Q.N.) - correct answer-
~(∃x)(Px • Qx) : : (∀x)(Px ⊃ ~Qx)
[~I ≡ E]
~(∃x)(Px) : : _________ (Q.N.) - correct answer- ~(∃x)(Ax)
: : (∀x)~(Px)
~(∃x)~(Px) : : _________ (Q.N.) - correct answer-
~(∃x)~(Ax) : : (∀x)(Px)
★ Conditional Exchange (Description) ★ - correct answer-
For a conditional, we can translate it to a disjunction with the
denial of the antecedent. This works because of Modus Ponens
and Modus Tollens. If P then Q is true under the following
circumstances: 1) P and Q are both true, 2) Q is true, 3) P and Q
are both false. if P then Q is false only when P is true but Q is
false. This is the same for the disjunction (~P v Q).
1. (~P v Q) when P and Q are true = (~P v Q) = true
2. (~P v Q) when only Q is true = (P v Q) = true
3. (~P v Q) when both are false = (P v ~Q) = true
, 4. (~P v Q) when P is true but Q is false = (~P v ~Q) = false
One disjunct MUST be true for the disjunction to be true.
1. Either the visiting team does not score, or I will eat my hat is
equivalent to if the visiting team scores, then I will eat my hat.
★ Conditional Exchange (Symbols) ★ - correct answer-
(P ⊃ Q) : : (~P v Q)
★ DeMorgan's (Description) ★ - correct answer- For
conjunctions and disjunctions, you can distribute a negation by
negating every part of the statement, including the operator.
Negating a disjunction makes it a conjunction.
Negating a conjunction makes it a disjunction.
The logic of this is as follows:
1a. (not P) and (not Q) is equivalent to not (P or Q)
1b. (not P) or (not Q) is equivalent to not (P and Q)
