Examination Questions And Answers English Work Sheet Page 7
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7C. Logical Equivalences
Use a truth table to determine which of the following pairs of sentence forms are
logically equivalent.
~ (p ⊃ q), p ⋅ ~ q
p ⊃ (q ⋅ r), (p ⊃ q) ⋅ (p ⊃ r)
1.
3.
~ (p ≡ q), (~ p ≡ q) ∨ (p ≡ ~ q)
~ [(p ∨ q) ⊃ p], ~ [(p ⊃ q) ∨ q]
2.
4.
C. Answers
1.
Equivalent
3.
Equivalent
2.
Equivalent
4.
Not Equivalent
D. Proving Validity of Argument Forms
Determine by truth table analysis which of the following argument forms are valid and
which are invalid:
1. (~ p ∨ q) ∨ (~ p ⋅ q)
1. (p ⋅ q) ≡ (q ⋅ r)
(1)
(3)
∴
∴
2. q ⊃ p /
2. ~ (r ⊃ ~ q) /
~ r ⊃ p
~ q
1. p ⊃ ~ (~ q ∨ r)
1. ~ (p ⋅ ~ q) ≡ ~ p
(2)
(4)
∴
2. ~ r ⊃ q /
~ p ⋅ q
/∴ (~ q ∨ p) ∨ (~ q ⊃ ~ p)
D. Answers
(1)
Invalid
(3)
Valid
(2)
Invalid
(4)
Valid
E. Short Truth Table Test for Invalidity
Use the short truth table method to show that the following arguments are invalid and
provide the truth-value assignments that show invalidity for each:
1. A ⊃ B
1. A ∨ (B ⋅ ~ C)
(1)
(3)
2. C ⊃ ~ B
1. A ∨ (B ⋅ ~ C)
(3)
2. ~ [A ⋅ ~ (C ∨ B)]
3. ~ C /∴ A
3. B ⊃ C
1. A ⊃ (B ∨ C)
(2)
4. ~ B /∴ ~ A
2. B ⊃ (C ⊃ D)
3. ~ D /∴ ~ A
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