5. Given p is false, q is true, and r is false, find the truth value of the statement (~p<-->~q)-->~r. Show step by step work.

To find the truth value of the given statement (~p<-->~q)-->~r, we will evaluate each part of the statement separately and then combine the results.

Step 1: Evaluate ~p
Since p is false, the negation of p (~p) will be true.

Step 2: Evaluate ~q
Since q is true, the negation of q (~q) will be false.

Step 3: Evaluate ~r
Since r is false, the negation of r (~r) will be true.

Step 4: Evaluate ~p<-->~q
The truth table for the biconditional (~p<-->~q) can be determined as follows:

| ~p | ~q | ~p<-->~q |
|-------|-------|----------|
| true | false | false |
|-------|-------|----------|

Since ~p is true and ~q is false, ~p<-->~q will be false.

Step 5: Evaluate (~p<-->~q)-->~r
Using the truth value from step 3, we can determine:

| ~p<-->~q | ~r | (~p<-->~q)-->~r |
|----------|-------|----------------|
| false | true | true |
|----------|-------|----------------|

Therefore, the truth value of the statement (~p<-->~q)-->~r is true.