Conditional Statement: Concept, Types & Examples

Conditional Statement is a part of mathematical reasoning which is simply understood as when a condition is put on something to get a return for something. Mathematical reasoning is one of the critical skills that is known to help students in analysing provided hypothesis without a particular meaning or context. Thus, to prove the hypothesis, scientific and factual-based derivatives and proofs are needed and this cannot be defined by individual opinion. In this case, the statement plays an important role by declaring if the sentence is true, false or neither both. Conditional Statements and Bi-conditional Statements are the two types of statements in the study of logic. For example, Anisha said, “If the rain stops, then I will go to school”. Here Anisha says she will go to school on a condition if the rain stops. 

Key Terms: Conditional Statement, Hypothesis, Conclusion, Converse, Inverse, Contrapositive Statement, Bi-conditional Statement

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Concept of Conditional Statement

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Conditional statement is understood as a statement that emphasises the two ideas which are dependent or follows each other. It is often simply understood as an if-then statement which is used in mathematical expressions. 

One such example is: “If you do your homework, then you will get good marks”. In this sentence, the idea of getting good marks is following doing your homework. These conditional statements are essential in declaring the mathematical deductions and logical reasoning clearly and rigorously.

Diving deep into the concept of conditional statement, we can classify the sentence into two portions: 

• Hypothesis

This is the initial plan which generally represents the first part of the conditional statement, usually starting with “if”. For example: “if Nandini eats mutton biryani, then Aditi will eat chicken biryani”, in this sentence, the part which starts with “if” denotes the hypothesis. The first part is depicting a hypothetical plan in case Nandini eats biryani.

• Conclusion

This is the second part of a conditional statement, which generally starts with “then” and is known to express the result of the plan/hypothesis. For example, in the above-mentioned example, the conclusion is “then Aditi will eat chicken biryani”. This depicts that because of the plan where Nandini is having mutton biryani, Aditi will be having chicken biryani.

Parts of Conditional Statement

Also check: Level of Significance

In general, the two parts of a conditional statement are represented by the variables p and q where p is the hypothesis and q is the conclusion. To understand the conditional relation between this p and q, an arrow mark (‎‎→) is used. So, in the above-mentioned example:

p = if Nandini eats mutton biryani

q = then Aditi will eat chicken biryani

So, p‎‎ → q

As mentioned earlier, in mathematics we need to derive the end result through scientific expressions. In the case of conditional statements, we have to evaluate the statements whether are true or false through certain formula. These formulas depend on the relationship between the hypothesis (p) and the conclusion (q) of the conditional statement.

Also check:

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Types of Conditional Statements

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Conditional statements can be broadly categorised into its 4 types which are as follows on the basis of the interrelationship among the hypothesis and conclusion denoting whether the conditional statement is true and false

• Converse of Statement

Converse statement is that type of conditional statement where the hypothesis and the conclusion used can be interchanged and thus depends on each other. In this kind of statement, both the hypothesis and the conclusion are considered true and so, the conditional statement is also considered true. For example, let our conditional statement be “if a population consists of 40% girls, then there must be 60% boys”. Here,

p= if the population has 40% girls

q= then there will be 60% boys

That is, p‎‎ → q

Then, if we interchange p and q, the converse conditional statement will be

If a population consists of 60% boys, then there must be 40% girls

That is, q‎‎ → p

• Inverse of Statement

The conditional statement which is expressed in negative words is termed as an inverse conditional statement. In this type of conditional statement, the hypothesis and the conclusion are turned negative. For instance, consider the statement “if a population does not consist of 40% girls, then there must not be 60% boys”.

That is ~p‎‎ → ~q

Also check: Important Questions for Mathematical Reasoning 

• Contrapositive Statement

Contrapositive conditional statement is the statement when we interchange the hypothesis and the conclusion but both of them are expressed in negative speech. In this kind of conditional statement, both the hypothesis and the conclusion tend to be true but are interchangeable and interlinked. For example, let our conditional statement be “If the sun does not rise in the east, then it does not set in the west”. Here,

p = If the sun does not rise in the east

q = then it does not set in the west

That is, p ‎‎→ q

Then if we interchange, the sentence will be a contrapositive conditional statement

If the sun does not set in the west, then it does not rise in the east”

That is, ~q‎‎ → ~p

• Bi-conditional Statement

In a bi-conditional statement, the use of “if-if” occurs which denotes that the hypothesis can be true only in the case if the conclusion is also true. That means, that if the conclusion is false, the entire conditional statement can be false. For example, let the conditional statement be “if he contacts me, then he need help”

The bi-conditional statement will be “he will contact me if and only if he will need help”

That is p ↔ q

For a clear understanding, a tabular description of the conditional statements have been provided with T denoting truth and F denoting False”

Also check: Truth Table

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Things to Remember

• A conditional statement is also termed implication. It helps us to take decisions based on certain conditions. It is also used in computer applications like JAVA.
• A conditional statement consists of 2 parts: the hypothesis (plan) and the conclusion (outcome).
• There are 4 kinds of conditional statements: converse, inverse, contrapositive and bi-conditional.
• Converse is where the hypothesis and the conclusion used can be interchanged and thus depends on each other.
• Inverse is the conditional statement expressed in negative words.
• Contrapositive conditional statement is when we interchange the hypothesis and the conclusion but both of them are expressed in negative speech
• In a bi-conditional statement, the use of “if-if” occurs which denotes that the hypothesis can be true only in the case if the conclusion is also true.