Feedback — Graded Quiz §2a Using Truth Tables to
Check for Logical Relations and Validity [v2]
You got a score of 5.00 out of 5.00.
Question 1
These questions will test your ability to use truth tables and to determine logical relations between
formulas from the language of propositional logic.
Consider the truth table for the formulas (A) and (B).
(A) ((q∨p)∨(p⊃p))
(B) ∼(∼(p∨q)&(r∨r))
What is the logical relation between these formulas?
Your Answer
Score
(A) logically implies (B)
(B) logically implies (A)
(A) and (B) are logically independent
(A) and (B) are logically equivalent
Correct
1.00
Total
1.00 / 1.0
Question Explanation
∼(∼(p∨q)&(r∨r)) logically implies formula ((q∨p)∨(p⊃p)). To see this consider any row of a
truth-table in which ∼(∼(p∨q)&(r∨r)) is true. In any such row ((q∨p)∨(p⊃p)) is also true.
But ∼(∼(p∨q)&(r∨r)) is not logically equivalent to ((q∨p)∨(p⊃p)) as there is a valuation which
makes ((q∨p)∨(p⊃p)) true and ∼(∼(p∨q)&(r∨r)) false, namely the following:
p0
q0
r1
Question 2
These questions will test your ability to use truth tables and to determine logical relations between
formulas from the language of propositional logic.
Consider the truth table for the formulas (A) and (B).
(A) ((q∨p)∨(p⊃p))
(B) (∼q⊃∼p)
What is the logical relation between these formulas?
Your Answer
(B) logically implies (A)
(A) and (B) are logically equivalent
Score
Correct
1.00
(A) and (B) are logically independent
(A) logically implies (B)
Total
1.00 / 1.0
Question Explanation
(∼q⊃∼p) logically implies formula ((q∨p)∨(p⊃p)). To see this consider any row of a truth-table in
which (∼q⊃∼p) is true. In any such row ((q∨p)∨(p⊃p)) is also true. But (∼q⊃∼p) is
not logically equivalent to ((q∨p)∨(p⊃p)) as there is a valuation which makes ((q∨p)∨(p⊃p)) true
and (∼q⊃∼p) false, namely the following:
p1
q0
Question 3
Consider the following truth table.
What does this truth table tell us about the following argument?
∼((r&r)∨p∨r), ∼(p⊃(q∨q∨q)) therefore (∼p∨∼r)
Your Answer
The argument is valid
The argument is invalid
Score
Correct
1.00
Cannot tell
Total
1.00 / 1.00
Question Explanation
As you can see, there's no row where the premises are true and the conclusion is false. As a result this
argument is valid.
Question 4
Consider the following truth table.
What does this truth table tell us about the following argument?
(∼q∨∼r), ∼((q⊃(p∨∼p))&r) therefore (∼q&∼r)
Your Answer
Score
Cannot tell
The argument is valid
The argument is invalid
Total
Correct
1.00
1.00 / 1.00
Question Explanation
As you can see there are rows of this truth table where the premises are true and the conclusion is false. As
a result this argument is invalid.
Question 5
Consider the following truth table.
What does this truth table tell us about the following argument?
∼(∼p⊃p), (q∨(q&∼p)∨p) therefore ((p⊃q)⊃(r∨r))
Your Answer
Score
The argument is valid
The argument is invalid
Correct
1.00
Cannot tell
Total
1.00 / 1.00
Question Explanation
As you can see there are rows of this truth table where the premises are true and the conclusion is false. As
a result this argument is invalid.