Q.Write logical expressions corresponding to the following statements in Python and evaluate the expressions (assuming variables num1, num2, num3, first, middle, last are already having meaningful values):

Boolean Expressions: From Intuition to Precision

Imagine a light switch. It has exactly two states: on or off. There is no dimmer, no half‑on, no third option. A Boolean expression is just a way of describing conditions that also have only two possible outcomes: true or false.

That’s the entire intuition. Every Boolean expression you will ever write is a question that the computer (or a circuit) answers with a clear yes or no.

The Building Blocks

A Boolean expression is built from three things:

1. Boolean variables – these are placeholders that can hold either true (1) or false (0). For example, A, B, rain, isWeekend.
2. Logical operators – these combine variables into questions. There are three fundamental ones:
   • AND (written as $\cdot$ or $\land$): “Are both conditions true?”
   • OR (written as $+$ or $\lor$): “Is at least one condition true?”
   • NOT (written as $\overline{A}$ or $\lnot A$): “Is the condition false?”
3. Constants – true (1) and false (0).

How They Work: The Truth Table

The simplest way to see what a Boolean expression means is to list every possible combination of its variables and compute the result. That list is called a truth table.

Take the expression $F = A + B$ (A OR B). There are $2^2 = 4$ possibilities:

The result is 1 whenever at least one input is 1. That’s the OR operation.

Now take $G = A \cdot B$ (A AND B):

Only when both are 1 does the result become 1.

And NOT simply flips the value: $\overline{0} = 1$, $\overline{1} = 0$.

Why This Matters

Boolean expressions are the language of digital circuits and computer logic. Every decision in a program – every if condition, every loop condition – reduces to a Boolean expression. When you write if (age >= 18 && hasID), the computer evaluates age >= 18 (true/false) and hasID (true/false), then combines them with AND to decide whether to let you in.

In exams, you will be asked to:

• Simplify Boolean expressions using laws (like $A + A \cdot B = A$).
• Derive expressions from truth tables.
• Draw logic gates from expressions.

But before any of that, the core idea is simple: a Boolean expression is a yes/no question built from yes/no variables.

The Precise Statement

That’s it. No hidden complexity. The entire subject of Boolean algebra is just the study of how these expressions behave and how to manipulate them – much like ordinary algebra, but with only two numbers and a different set of rules.