How can I prove that following is a tautology (using laws of logical equivalences)

Question

$(p → q) ∧ (q → r) → (p → r)$

Without Truth Tables!

Answer 1

Answer in image uploaded. Contact me for further description

Comments

If you can record a video, and explain step by step, that would be much better. It could be confusing how you conclude line 6 from line 5,  but if you just record a video and talk over it while solving, that will be clarified. In addition, I removed your personal information such as student number from your post. Please do not include them while posting publicly.

Answer 2

i solved the brackets first.

Comments

Can you solve it without using Truth Tables? In the exam, you are probably not allowed to prove it using truth tables and you have to just use logical equivalences.