Question 1
Given: p → q, p
What can you validly derive?
Rule: Modus Ponens (→-elimination)
If P → Q and P are true, Q must be true.
Answer: q
If P → Q and P are true, Q must be true.
Answer: q
Natural Deduction: Worksheet 10 - Expert Practice Natural Deduction EXPERT
Ready to master Natural Deduction? This accuracy focus 👑 worksheet (10/10) presents 20 expert-level challenges. Focus area: application-based learning. Learn to solve natural deduction reasoning tricks, handle fast natural deduction solving, and perfect natural deduction mastery with our step-by-step solutions.
What you'll learn in this worksheet:
- Understand the logic behind fast natural deduction solving
- Learn step-by-step approaches to application-based learning
- Achieve mastery with the most difficult problem types
- Perfect your speed and accuracy under time pressure
- Master natural deduction reasoning tricks through focused practice
Your progress through Natural Deduction
Worksheet 10 of 10 (100% complete)
Question 2
Given: p ∨ q, ¬p
What can you validly derive?
Rule: Disjunctive Syllogism
If P ∨ Q is true and P is false, then Q must be true.
Answer: q
If P ∨ Q is true and P is false, then Q must be true.
Answer: q
Question 3
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 4
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 5
Given: p, q
What can you validly derive?
Rule: Conjunction Introduction (∧-intro)
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
Question 6
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 7
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 8
Given: p ∨ q, ¬p
What can you validly derive?
Rule: Disjunctive Syllogism
If P ∨ Q is true and P is false, then Q must be true.
Answer: q
If P ∨ Q is true and P is false, then Q must be true.
Answer: q
Question 9
Given: p → q, p
What can you validly derive?
Rule: Modus Ponens (→-elimination)
If P → Q and P are true, Q must be true.
Answer: q
If P → Q and P are true, Q must be true.
Answer: q
Question 10
Given: p → q, ¬q
What can you validly derive?
Rule: Modus Tollens
If P → Q and Q is false, then P must be false.
Answer: ¬p
If P → Q and Q is false, then P must be false.
Answer: ¬p
Question 11
Given: p → q, ¬q
What can you validly derive?
Rule: Modus Tollens
If P → Q and Q is false, then P must be false.
Answer: ¬p
If P → Q and Q is false, then P must be false.
Answer: ¬p
Question 12
Given: p → q, p
What can you validly derive?
Rule: Modus Ponens (→-elimination)
If P → Q and P are true, Q must be true.
Answer: q
If P → Q and P are true, Q must be true.
Answer: q
Question 13
Given: p → q, ¬q
What can you validly derive?
Rule: Modus Tollens
If P → Q and Q is false, then P must be false.
Answer: ¬p
If P → Q and Q is false, then P must be false.
Answer: ¬p
Question 14
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 15
Given: p, q
What can you validly derive?
Rule: Conjunction Introduction (∧-intro)
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
Question 16
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
Question 17
Given: p → q, p
What can you validly derive?
Rule: Modus Ponens (→-elimination)
If P → Q and P are true, Q must be true.
Answer: q
If P → Q and P are true, Q must be true.
Answer: q
Question 18
Given: p → q, ¬q
What can you validly derive?
Rule: Modus Tollens
If P → Q and Q is false, then P must be false.
Answer: ¬p
If P → Q and Q is false, then P must be false.
Answer: ¬p
Question 19
Given: p, q
What can you validly derive?
Rule: Conjunction Introduction (∧-intro)
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
If you have P and you have Q, you can combine them into P ∧ Q.
Answer: p ∧ q
Question 20
Given: p
What can you validly derive?
Rule: Disjunction Introduction (∨-intro)
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
If P is true, then P ∨ Q is true for any Q (addition rule).
Answer: p ∨ q
🏆 Congratulations! You've mastered Natural Deduction - all 10 worksheets completed!