Questions: p q (∼q ∨ p) ∨ ∼(∼q ∧ p) T T □ T F □ F T □ F F □

p q (∼q ∨ p) ∨ ∼(∼q ∧ p) T T □ T F □ F T □ F F □
Transcript text: \begin{tabular}{|c|c|c|} \hline$p$ & $q$ & $(\sim q \vee p) \vee \sim(\sim q \wedge p)$ \\ \hline$T$ & $T$ & $\square$ \\ \hline$T$ & $F$ & $\square$ \\ \hline F & T & $\square$ \\ \hline F & F & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify the logical operators and variables in the expression

The given expression is: ( not True or True) or not ( not True and True) with p = True and q = True.

Step 2: Understand the precedence of operators

The precedence of operators is NOT (∼) > AND (∧) > OR (∨) > IMPLIES (→).

Step 3: Evaluate the expression step by step

After substituting p and q with their values, the expression to evaluate is: ( not True or True) or not ( not True and True).

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: ( not True or True) or not ( not True and True).

Step 5: Evaluate according to precedence

Evaluating the expression according to the precedence of operators.

Final Answer:

The truth value of the given logical expression is: ^True^.

Step 1: Identify the logical operators and variables in the expression

The given expression is: ( not False or True) or not ( not False and True) with p = True and q = False.

Step 2: Understand the precedence of operators

The precedence of operators is NOT (∼) > AND (∧) > OR (∨) > IMPLIES (→).

Step 3: Evaluate the expression step by step

After substituting p and q with their values, the expression to evaluate is: ( not False or True) or not ( not False and True).

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: ( not False or True) or not ( not False and True).

Step 5: Evaluate according to precedence

Evaluating the expression according to the precedence of operators.

Final Answer:

The truth value of the given logical expression is: ^True^.

Step 1: Identify the logical operators and variables in the expression

The given expression is: ( not True or False) or not ( not True and False) with p = False and q = True.

Step 2: Understand the precedence of operators

The precedence of operators is NOT (∼) > AND (∧) > OR (∨) > IMPLIES (→).

Step 3: Evaluate the expression step by step

After substituting p and q with their values, the expression to evaluate is: ( not True or False) or not ( not True and False).

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: ( not True or False) or not ( not True and False).

Step 5: Evaluate according to precedence

Evaluating the expression according to the precedence of operators.

Final Answer:

The truth value of the given logical expression is: ^True^.

Step 1: Identify the logical operators and variables in the expression

The given expression is: ( not False or False) or not ( not False and False) with p = False and q = False.

Step 2: Understand the precedence of operators

The precedence of operators is NOT (∼) > AND (∧) > OR (∨) > IMPLIES (→).

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