Questions: Complete the truth table. p q ~q p ∧ ~q p → q ~(p → q) ---------------------------------- T T T F

Complete the truth table. p q ~q p ∧ ~q p → q ~(p → q) ---------------------------------- T T T F
Transcript text: Complete the truth table. \begin{tabular}{|c|c|c|c|c|c|} \hline$p$ & $q$ & $\sim q$ & $p \wedge \sim q$ & $p \rightarrow q$ & $\sim(p \rightarrow q)$ \\ \hline$T$ & $T$ & & & & \\ \hline T & F & & & & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify all logical variables

The logical variables involved are: p, q.

Step 2: Determine all possible combinations of truth values

For 2 variables, there are 4 combinations.

Step 3 & 4: Compute the truth value of the expression for each combination

The truth table is as follows: | p | q | Result | |+|+|+| | False | False | (False, False, -1) | | False | True | (False, True, -2) | | True | False | (True, True, -2) | | True | True | (True, True, -2) |

Final Answer:

The complete truth table has been generated above.

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