Construct a truth table for (~PVq)___> q

To construct a truth table for the logical expression (~PVq) → q, we need to list all possible combinations of truth values for the variables P and q, and then evaluate the entire expression for each combination.

Let's break it down step by step:

Step 1: Identify the variables

The expression (~PVq) → q consists of two variables: P and q.

Step 2: List all possible combinations of truth values

Since we have 2 variables, there are 2^2 = 4 possible combinations. Let's denote the combinations using binary codes:

Combination 1: P = 0, q = 0 (written as 00 in binary)
Combination 2: P = 0, q = 1 (01)
Combination 3: P = 1, q = 0 (10)
Combination 4: P = 1, q = 1 (11)

Step 3: Evaluate the expression for each combination

Now, let's evaluate the expression (~PVq) → q for each combination:

Combination 1: P = 0, q = 0
(~0V0) → 0
(1V0) → 0
1 → 0
0 (False)

Combination 2: P = 0, q = 1
(~0V1) → 1
(1V1) → 1
1 → 1
1 (True)

Combination 3: P = 1, q = 0
(~1V0) → 0
(0V0) → 0
0 → 0
1 (True)

Combination 4: P = 1, q = 1
(~1V1) → 1
(0V1) → 1
1 → 1
1 (True)

Step 4: Create the truth table

Based on the evaluations above, we can construct the truth table for (~PVq) → q:

| P | q | (~PVq) → q |
---------------------
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

This truth table shows the result (True or False) for the logical expression (~PVq) → q for each combination of truth values of P and q.