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: \[ \begin{array}{l|l|l|l} p & q & \sim q \leftrightarrow p & \sim q \rightarrow p \end{array} \] T T $\square$ $\square$ T F $\square$ $\square$ F T $\square$ $\square$ F F $\square$ $\square$
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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 <= 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 <= True.

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: not True <= 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: ^False^.

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

The given expression is: not False <= 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 <= True.

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: not False <= 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: ^False^.

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

The given expression is: not True <= 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 <= False.

Step 4: Apply the truth values of p and q

Substituting the given truth values, we get: not True <= 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 <= 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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