5. Maria says 1, 2, 3, 4, 6, and 12 are all the factors of a number. What is the number?
2 answers:
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Answer:
1. (P --> Q) & R
2. P --> (Q & R)
3. (P&Q) --> R
4. P & (Q --> R)
5. P --> (Q --> R)
6. (P --> Q) & (R --> Q)
7. (P v R) --> Q
8. P v (Q --> R)
9. (P v Q) --> R
10. P --> (Q v R)
Explanation:
If Parsons signs the papers then Quincy will go to jail, and Rachel will file an appeal:
(P --> Q) & R
If Parsons signs the papers, then Quincy will go to jail and Rachel will file an appeal:
P --> (Q & R)
If Parsons signs the papers and Quincy goes to jail then Rachel will file an appeal:
(P&Q) --> R
If Parsons signs the papers and if Quincy goes to jail Rachel will file an appeal:
P & (Q --> R)
If Parsons signs the papers then if Quincy goes to jail Rachel will file an appeal:
P --> (Q --> R)
If Parsons signs the papers Quincy goes to jail, and if Rachel files an appeal Quincy goes to jail:
(P --> Q) & (R --> Q)
Quincy goes to jail if either Parsons signs papers or Rachel files an appeal:
(P v R) --> Q
Either Parsons signs the papers or, if Quincy goes to jail, then Rachel will file an appeal:
P v (Q --> R)
If either Parsons signs the papers or Quincy goes to jail then Rachel will file an appeal:
(P v Q) --> R
If Parsons signs the papers then either Quincy will go to jail or Rachel will file an appeal:
P --> (Q v R)
I have added truth table in attachment.
All possible conditions for each statements are in truth table with both true and false cases of P,Q,R.
