CIS 160 Boolean logic

• Use Boolean operators in expressions
• Complete a truth table
• Use relational operators in expressions
• Use logical operators in expressions

• Boolean logic was developed by George Boole in the mid 1800s
• Boolean logic expressions evaluate to true or false
• the primary operations are NOT, AND, and OR
• Java uses the operator ! for NOT
• Java uses the operator && for AND
• Java uses the operator || for OR
• NOT (! in Java) reverses the value of its operand ("NOT true" evaluates to false, "NOT false" evaluates to true)
• AND (&& in Java) takes two operands; it evaluates to true if both operands are true, otherwise it evaluates to false
• OR (|| in Java) also takes two operands; it evaluates to true if either operand is true; it evaluates to false if and only if BOTH operands are false

A	B	!A	!B	A && B	A || B
true	true	false	false	true	true
true	false	false	true	false	true
false	true	true	false	false	true
false	false	true	true	false	false

There are a couple of extremely useful transformations for propositional logic that seem to have been known since at least the time of Aristotle. Augustus De Morgan introduced the formal version of the following two transformation laws for propositional logic in the 1800s.

• NOT (A OR B) is equivalent to (NOT A) AND (NOT B)
• NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

A	B	!(A || B)	(!A) && (!B)	!(A && B)	(!A) || (!B)
true	true	false	false	false	false
true	false	false	false	true	true
false	true	false	false	true	true
false	false	true	true	true	true

There are six relational operators. All will evaluate to true or false.

• < (less than)
• <= (less than or equal)
• > (greater than)
• >= (greater than or equal)
• == (equal to)
• != (not equal to)

DisplayTruthTable.java: displays a truth table