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VinnyW

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- TL;DR Summary
- How to simplify ((p ↓ p) ↓ q) ↓ (p ↓ p) ↓ q) ) to F ↓ (( F ↓ q ) ↓ q ), whereas p and q are atomic propositions and F, probably, is contradiction.

I hope someone can help me or point me in the right direction.

I am reading

The question is (Section 1.3 Foundations: Logic and Proofs. Question 51)

I know

and

By combining them, I got the answer:

which is the same answer as the one in the solution manual; however, the manual also lists:

I know

How can I simplify

to

I am reading

*by***Discrete Mathematics with its Applications***. I am trying to self learn discrete math. I am actually able to do most questions but I have a question about a solution (not the question itself.)***Rosen**The question is (Section 1.3 Foundations: Logic and Proofs. Question 51)

**Question**:**Find a compound proposition logically equivalent to p → q using only the logical operator ↓**

My answer:My answer

I know

**p → q ≡ ¬ p ∨ q**and

**p ↓ p ≡ ¬ p**By combining them, I got the answer:

**((p ↓ p) ↓ q) ↓ (p ↓ p) ↓ q) )**which is the same answer as the one in the solution manual; however, the manual also lists:

**F ↓ (( F ↓ q ) ↓ q )**I know

**F**is contradiction.How can I simplify

**((p ↓ p) ↓ q) ↓ (p ↓ p) ↓ q) )**to

**F ↓ (( F ↓ q ) ↓ q )**