Question 1
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
Master Natural Deduction - Beginner Level Problems Natural Deduction BEGINNER
Excel in competitive exams with this skill builder ⚡ worksheet on Natural Deduction. Worksheet 3 of 10 contains 20 beginner-level problems. Target your step-by-step problem solving skills while practicing natural deduction practice, natural deduction for competitive exams, and how to solve natural deduction.
What you'll learn in this worksheet:
- Master natural deduction practice through focused practice
- Understand the logic behind natural deduction for competitive exams
- Learn step-by-step approaches to step-by-step problem solving
- Develop systematic problem-solving habits
- Strengthen your foundational understanding
Your progress through Natural Deduction
Worksheet 3 of 10 (22% complete)
Question 2
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 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 → 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 5
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 6
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 7
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 8
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 9
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 10
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 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
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 13
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 14
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 15
Given: p ∧ q
What can you validly derive?
Rule: Simplification (∧-elimination)
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
Question 16
Given: p ∧ q
What can you validly derive?
Rule: Simplification (∧-elimination)
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
Question 17
Given: p ∧ q
What can you validly derive?
Rule: Simplification (∧-elimination)
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
Question 18
Given: p ∧ q
What can you validly derive?
Rule: Simplification (∧-elimination)
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
From a conjunction P ∧ Q, you can derive P (or Q) alone.
Answer: p
Question 19
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 20
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
📝 Continue your Natural Deduction practice. Worksheet 3 focuses on step-by-step problem solving.