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5 votes
Construct a truth table for the statement (~ pVq) →q.

asked
User Bowheart
by
8.2k points

1 Answer

4 votes

Here is the truth table for the statement (~ p V q) → q:

```

p q ~p ~p V q (~p V q) → q

---------------------------------------

T T F T T

T F F F T

F T T T T

F F T F T

```

In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").

To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.

We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.

answered
User SuperK
by
8.3k points
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