Question 1
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
Natural Deduction - Absolute-Beginner Level: core concept mastery Natural Deduction ABSOLUTE BEGINNER
This skill primer 🌟 worksheet focuses on Natural Deduction - a key topic in Logical Connectives. You'll solve 20 absolute-beginner-level problems (Worksheet 1 of 10). The primary focus is on core concept mastery. Master natural deduction problems, natural deduction reasoning questions, and natural deduction practice through systematic practice.
What you'll learn in this worksheet:
- Master natural deduction problems through focused practice
- Understand the logic behind natural deduction reasoning questions
- Learn step-by-step approaches to core concept mastery
- Start with the absolute basics - no prior knowledge needed
- Learn fundamental concepts with simple examples
Your progress through Natural Deduction
Worksheet 1 of 10 (0% complete)
Question 2
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 3
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 4
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 5
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 6
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 7
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 8
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 9
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 10
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 11
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 12
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 13
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 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
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 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: 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 18
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 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: 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
🌟 Start your Natural Deduction journey here! Build strong foundations with this beginner worksheet.