p→q; p→r; ¬q∨¬r; ∴¬p please prove using natural deduction.

1.           basic assumption

2.     `p -> r`      basic assumption            

3.  `not q vv not r`    basic assumption(goal:`not p` )

In order to proof this we will need to divide it into two mini proofs: 

Mini proof 1: 

4.  `not q`               (Assume `vv E`    to prove `p`)

5   `not p`               ( `-> E`   lines 1,4)` `

Mini proof 2: 

6.   `not r`                (Assume  `vv E`   to prove `p`)

7.  `not p`                 (`-> E` lines 2,6)

CONCLUSION: (now we can show the proof)

8. `not p`                        (`vv E`   lines3, 4-5, 6-7)

This is how we proof by natural deduction.