For statements p,q and r use a truth table to show that p implies (q or r) and ((not r)and p) not p)implies q?

To create a truth table for the statements p, q, and r, we need to consider all possible combinations of truth values for p, q, and r. Since there are 2 possible truth values (True or False) for each statement, there will be a total of 2^3 = 8 rows in the truth table.

Let's start by listing all possible combinations of truth values for p, q, and r:

| p | q | r |
|------|------|------|
| True | True | True |
| True | True | False |
| True | False| True |
| True | False| False|
| False| True | True |
| False| True | False |
| False| False| True |
| False| False| False|

Now, let's evaluate the statements p implies (q or r) and ((not r) and p) not p) implies q for each row of the truth table:

1. p implies (q or r):
- For the first row (True, True, True):
p implies (q or r) = True implies (True or True) = True implies True = True
- For the second row (True, True, False):
p implies (q or r) = True implies (True or False) = True implies True = True
- For the third row (True, False, True):
p implies (q or r) = True implies (False or True) = True implies True = True
- For the fourth row (True, False, False):
p implies (q or r) = True implies (False or False) = True implies False = False
- For the fifth row (False, True, True):
p implies (q or r) = False implies (True or True) = False implies True = True
- For the sixth row (False, True, False):
p implies (q or r) = False implies (True or False) = False implies True = True
- For the seventh row (False, False, True):
p implies (q or r) = False implies (False or True) = False implies True = True
- For the eighth row (False, False, False):
p implies (q or r) = False implies (False or False) = False implies False = True

2. ((not r) and p) not p) implies q:
- For the first row (True, True, True):
((not r) and p) not p) implies q = ((not True) and True) not True) implies True = (False and True) not True) implies True = False not True) implies True = True implies True = True
- For the second row (True, True, False):
((not r) and p) not p) implies q = ((not False) and True) not True) implies True = (True and True) not True) implies True = True not True) implies True = True implies True = True
- For the third row (True, False, True):
((not r) and p) not p) implies q = ((not True) and True) not True) implies False = (False and True) not True) implies False = False not True) implies False = True implies False = False
- For the fourth row (True, False, False):
((not r) and p) not p) implies q = ((not False) and True) not True) implies False = (True and True) not True) implies False = True not True) implies False = True implies False = False
- For the fifth row (False, True, True):
((not r) and p) not p) implies q = ((not True) and False) not False) implies True = (False and False) not False) implies True = False not False) implies True = True implies True = True
- For the sixth row (False, True, False):
((not r) and p) not p) implies q = ((not False) and False) not False) implies True = (True and False) not False) implies True = False not False) implies True = True implies True = True
- For the seventh row (False, False, True):
((not r) and p) not p) implies q = ((not True) and False) not False) implies False = (False and False) not False) implies False = False not False) implies False = True implies False = False
- For the eighth row (False, False, False):
((not r) and p) not p) implies q = ((not False) and False) not False) implies False = (True and False) not False) implies False = False not False) implies False = True implies False = False

Now, let's