What are conditionals? When they are required in a program?

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Q. What are conditionals? When they are required in a program?

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Concept understanding — Conditional Statements

Conditional Statements: From Intuition to Precision

Imagine you're making a promise to a friend. You say: "If it rains tomorrow, I will give you a ride." That's a conditional statement — a promise that depends on a condition. The whole statement is about what happens if the condition is true.

Now, when does your promise get broken? Only if it rains and you don't give the ride. If it doesn't rain, you haven't broken anything — you never promised to give a ride in sunshine. And if it rains and you do give the ride, you kept your word. That's the core intuition.

The Formal Definition

In mathematics and logic, a conditional statement is an "if-then" statement. It has two parts:

Hypothesis (the "if" part): usually denoted $p$
Conclusion (the "then" part): usually denoted $q$

We write it as:

p \rightarrow q

Read as: "if $p$ , then $q$ " or " $p$ implies $q$ ".

p \rightarrow q

The truth of the whole statement depends only on one forbidden situation: when $p$ is true but $q$ is false. In every other case, the conditional is considered true.

The Truth Table

Here is the complete truth table for $p \rightarrow q$ :

$p$	$q$	$p \rightarrow q$
T	T	T
T	F	F
F	T	T
F	F	T

The only row that gives "false" is the second one — true hypothesis, false conclusion. Everything else is true.

Watch out

The last two rows often feel strange at first. If $p$ is false, the conditional is automatically true, regardless of $q$ . This is called vacuous truth. Think of it this way: if the condition never happens, the promise was never tested, so it cannot be broken.

Why This Matters

Conditional statements are the backbone of mathematical reasoning. Every theorem is a conditional: "If a triangle has two equal sides, then it has two equal angles." Every proof works by assuming the hypothesis and showing the conclusion must follow.

They also appear in everyday logic, programming (if-statements), and even legal contracts. Once you see the pattern, you'll notice conditionals everywhere.

Tip

To check whether $p \rightarrow q$ is true, ask yourself: "Can I find a case where $p$ is true but $q$ is false?" If yes, the conditional is false. If no such case exists, it's true — even if $p$ never happens.

Related Forms You'll Meet

From a conditional $p \rightarrow q$ , three other statements are commonly built: …

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Conditionals are statements that let a program choose between alternative actions based on whether a condition (a true/false test) holds — the if / if-else / if-elif-else constructs.

They are required whenever a program must make a decision — i.e. when different inputs or situations demand different actions: validating input, classifying values, choosing a formula, branching a menu.

age = int(input("Enter age: "))
if age >= 18:
    print("Eligible to vote")
else:
    print("Not eligible yet")
``` …

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Conditionals are decision-making statements — a condition is evaluated to true or false, and the program executes different statements accordingly; they are needed wherever the flow of a program must depend on the data.

What conditionals are. By default, statements run sequentially, one after another. A conditional breaks that straight line: it evaluates a condition — an expression that is either true or false (usually built with relational operators like >, <=, == and logical operators AND/OR/NOT) — and selects which statements execute next. The standard forms are:

IF — do something only when the condition is true.
IF–ELSE — do one thing when true, another when false.
IF–ELSE IF–ELSE (ladder) — choose one among many alternatives.

IF condition THEN
    statements          (run only when condition is true)
ELSE
    other statements    (run only when condition is false)
END IF

When they are required. Whenever a program must make a decision — the same program has to behave differently for different data. Typical situations:

Classification: pass/fail from marks, even/odd, grade bands, tariff slabs.
Validation: accept an input only if it is in range, else reject it.
Choosing a computation: e.g. avoid dividing when the divisor is 0.
Menus and options: run the action matching the user's choice.

Example (Python)

num = int(input("Enter a number: "))
if num % 2 == 0:
    print("Even number")
else: …

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Q.What are conditionals? When they are required in a program?

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