Question 1
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
Master Natural Deduction - Intermediate-Advanced Level Problems Natural Deduction INTERMEDIATE ADVANCED
Excel in competitive exams with this self assessment worksheet on Natural Deduction. Worksheet 7 of 10 contains 20 intermediate-advanced-level problems. Target your accuracy improvement skills while practicing natural deduction shortcut methods, natural deduction bank exam questions, and natural deduction ssc cgl.
What you'll learn in this worksheet:
- Master natural deduction shortcut methods through focused practice
- Understand the logic behind natural deduction bank exam questions
- Learn step-by-step approaches to accuracy improvement
- Master complex problem variations and edge cases
- Develop advanced shortcut techniques
Your progress through Natural Deduction
Worksheet 7 of 10 (66% 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 ∧ 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 4
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 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 → 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: 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 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, ¬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 → 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 ∧ 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 12
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 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: 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
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 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, ¬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 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
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