Complete Guide to Mastering Logic and Truth Tables

• Conjunction (AND) denoted by \(\land\): If both \( p \) and \( q \) are true, then \( p \land q \) is true.
• Disjunction (OR) denoted by \(\lor\): If either \( p \) or \( q \) is true, then \( p \lor q \) is true.
• Negation (NOT) denoted by \(\neg\): If \( p \) is true, then \(\neg p \) is false and vice versa.
• Conditional (IF…THEN) denoted by \(\rightarrow\): “If \( p \) then \( q \)” is false only when \( p \) is true and \( q \) is false.
• Biconditional (IF AND ONLY IF) denoted by \(\leftrightarrow\): True if both \( p \) and \( q \) have the same truth value.

• List all possible combinations of truth values for the statements involved.
• Evaluate the compound statement for each combination.

Examples

Practice Questions:

1. Construct the truth table for the statement \( \neg p \land q \).
2. Evaluate the truth table for the biconditional statement \( p \leftrightarrow q \).
3. Determine the truth value of the statement \( (p \land q) \lor \neg p \) when \( p \) is true and \( q \) is false.

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1. Truth Table for \( \neg p \land q \)

   \( p \)	\( q \)	\( \neg p \land q \)
   T	T	F
   T	F	F
   F	T	T
   F	F	F

2. Truth Table for \( p \leftrightarrow q \)

   \( p \)	\( q \)	\( p \leftrightarrow q \)
   T	T	T
   T	F	F
   F	T	F
   F	F	T

3. The truth value of \( (p \land q) \lor \neg p \) when \( p \) is true and \( q \) is false is True.

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