Equivalent Boolean Expressions

Equivalent Boolean Expressions

Defining Boolean Expressions

  • A Boolean expression in computer science is an expression that results in a Boolean value, either true or false.
  • Boolean expressions utilise logical operators such as && (AND), || (OR) and ! (NOT) in their syntax.

Equivalent Boolean Expressions

  • Two Boolean expressions are considered equivalent if they yield the same result regardless of the values inputted.
  • There are various rules and laws, based on mathematical logic, that govern these equivalences.

De Morgan’s Laws

  • De Morgan’s Laws are widely used to create equivalent Boolean expressions.
  • The negation of a conjunction: !(A && B) is equivalent to (!A || !B).
  • The negation of a disjunction: !(A || B) is equivalent to (!A && !B).

Identity Laws

  • Identity Laws in Boolean algebra represent basic truths of Boolean logic.
  • Law of Identity: A || false is equivalent to A and A && true is equivalent to A.
  • Law of Negation: A || !A is equivalent to true and A && !A is equivalent to false.

Double Negative

  • According to the Double Negative Law, a double negation results in the initial expression: !!A is equivalent to A.

Distributive Laws

  • Distributive Laws allow logical operators to be distributed over parentheses:
  • Law of distribution for AND operator: A && (B || C) is equivalent to (A && B) || (A && C).
  • Law of distribution for OR operator: A || (B && C) is equivalent to (A || B) && (A || C).

Importance of Understanding Equivalent Boolean Expressions

  • Understanding equivalent Boolean expressions is fundamental to optimising code and debugging logic errors.
  • It enhances the clarity of code and improves computer efficiency.

The ‘if’ Statement

Basic Syntax

  • The ‘if’ statement in Java is used to test a condition followed by one or more statements. The structure is: if (Boolean_expression) { Statement(s) }.
  • If the Boolean expression evaluates to true, the block of code inside the ‘if’ statement will be executed.

‘else’ Statement

  • An else statement can be combined with an ‘if’ statement. It is executed when the Boolean expression is false.
  • Using ‘if’/’else’ statements allows the program to make decisions and execute different blocks of code based on different conditions.

‘else if’ Statement

  • A chain of ‘else if’ statements can be used when multiple conditions need to be evaluated.
  • In an ‘else if’ chain, Java stops at the first condition that is true, and the rest of the conditions are not evaluated.

Nested ‘if’ Statements

  • Nested ‘if’ statements mean an ‘if’ statement inside another ‘if’ statement.
  • Nested ‘if’ statements can test multiple conditions and execute complex decision-making structures.

Importance of ‘if’ Statements

  • Mastery of the use of ‘if’ statements is key to building logical algorithms and implementing efficient decision-making structures in code.