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Natural Deduction - Intermediate Level: tricky scenarios handling Natural Deduction INTERMEDIATE

This expert challenge 📈 worksheet focuses on Natural Deduction - a key topic in Logical Connectives. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve natural deduction, natural deduction tricks, and natural deduction shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Natural Deduction
Worksheet 5 of 10 (44% complete)

Question 1

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

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

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

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

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

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

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

Question 13

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

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

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

Question 16

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

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

Question 18

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

Question 19

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

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
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