Complete Guide to Mastering Logic and Truth Tables

Logic assigns every statement a truth value of true or false. A truth table lists every combination of inputs and the resulting output, which makes the behavior of and, or, and not completely explicit.

• 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.

Worked examples: building a truth table

Practice questions on logic and truth tables

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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