Answer all four questions correctly or you will get a bad review. Answer all 8 parts of number 4

1. Use logical equivalence to verify: (p((p+q)))+(pq)=p 2. Verify ((r>q)>p)((ppq)>r). 3. For exercise \# 5 on page 18 of DMOI, suppose you believe the _converse_ of the implication stated in italics is true. Answer the question regarding the five statements a) e). 4. Given the following premises from steps 1) to 7), use logic to reason about the conclusion 8). Justify your reasoning. 1. pq 2. r+s 3. s>t 4. q+s 5. s 6. (pr)>u 7. w+t 8. uW