Question

When we symbolize a claim, we're displaying its truth-functional structure. Show that you can figure out the structures of the following claims by symbolizing them. Use these letters for the first ten items:

use the symbols ~, &, V, and -->. We suggest that, at least, at first, you can make symbolization a two-stage process: first replace simple parts of claims with letters; then, replace logical words with logical symbols, and add parentheses as required. We'll do an example in two stages to show you what we mean.
most signs you need to show the truth-functional relationships are on your keyboard; for 'if-then', use the > sign that is above the . on your keyboard.

Example:
If Parsons signs the papers, then Quincy will go to jail but Rachel will not file an appeal.
Stage 1: If P, then Q but ~R.
Stage 2: P --> (Q & ~R)

3. If Parsons signs the papers and Quincy goes to jail then Rachel will file an appeal.

4. Parsons signs the papers and if Quincy goes to jail Rachel will file an appeal.

6. If Parsons signs the papers Quincy goes to jail, and if Rachel files an appeal Quincy goes to jail.

7. Quincy goes to jail if either Parsons signs papers or Rachel files an appeal.

8. Either Parsons signs the papers or, if Quincy goes to jail, then Rachel will file an appeal.

9. If either Parsons signs the papers or Quincy goes to jail then Rachel will file an appeal.

10. If Parsons signs the papers then either Quincy will go to jail or Rachel will file an appeal.

Construct full truth tables or use the short truth-table method to determine which of the following arguments are valid.

For example:

L v (W -> S)
P v ~S
~L -> W
P

Answer 1

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)

Step-by-step 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.