Question #314708

Determine whether this proposition is a tautology.

[(p → q) Ù (q → r)] → (p→ r) 


1
Expert's answer
2022-03-20T06:42:23-0400

Let p=1,q=0,r=0. Then

pq=0pq=0qr=1(pq)(qr)=1((pq)(qr))(pr)=0p\rightarrow q=0\\ p\rightarrow q=0\\ q\rightarrow r=1\\ (p\rightarrow q)\lor (q\rightarrow r)=1\\ ((p\rightarrow q)\lor (q\rightarrow r))\rightarrow (p\rightarrow r)=0

The formula is not a tautology.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS