Assembly Election Results Overview

In this assembly election, we are given the number of seats won by different political parties and independent candidates. We need to analyze these numbers to determine which of the given statements must be incorrect.

Here is the breakdown of seats won:

• Party A: 30 seats
• Party B: 25 seats
• Party C: 20 seats
• Party D: 10 seats
• Party E: 4 seats
• Independents: 9 seats

First, let's find the total number of seats in this assembly election.

Total seats = Seats (A) + Seats (B) + Seats (C) + Seats (D) + Seats (E) + Seats (Independents)

Total seats = $30 + 25 + 20 + 10 + 4 + 9 = 98$ seats.

Majority Calculation

To form a government, a party or a coalition of parties needs to have a majority of the total seats. A majority is more than half of the total seats.

Majority seats = $\left\lfloor \frac{\text{Total seats}}{2} \right\rfloor + 1$

Majority seats = $\left\lfloor \frac{98}{2} \right\rfloor + 1 = 49 + 1 = 50$ seats.

So, 50 seats are required to form a majority government.

Analyzing Statements Based on Election Data

Let's evaluate each given statement based on the data and the majority requirement:

Party Majority Check (Statement 1)

Statement 1: "No party has majority."

We check if any single party has 50 or more seats:

• Party A: 30 seats (Less than 50)
• Party B: 25 seats (Less than 50)
• Party C: 20 seats (Less than 50)
• Party D: 10 seats (Less than 50)
• Party E: 4 seats (Less than 50)

Since no single party has 50 or more seats, the statement "No party has majority" is TRUE.

Coalition Formation A and C (Statement 2)

Statement 2: "A and C together can form the government."

This means we check if Party A and Party C combined have a majority.

Seats (A and C together) = Seats (A) + Seats (C)

Seats (A and C together) = $30 + 20 = 50$ seats.

Since 50 seats is exactly the number required for a majority, the coalition of A and C can form the government. The statement "A and C together can form the government" is TRUE.

Coalition Formation A, D, and Independents (Statement 3)

Statement 3: "A and D with the support of independents get the majority."

This means we check if Party A, Party D, and the Independents combined have a majority.

Seats (A, D, and Independents together) = Seats (A) + Seats (D) + Seats (Independents)

Seats (A, D, and Independents together) = $30 + 10 + 9 = 49$ seats.

The required majority is 50 seats. Since 49 seats is less than 50 seats, this coalition does NOT get the majority. The statement "A and D with the support of independents get the majority" is FALSE.

MLA from E as Chief Minister (Statement 4)

Statement 4: "An MLA from E can become Chief Minister."

The Chief Minister is typically the leader of the party or coalition that commands a majority in the assembly. While it is most common for the leader of the largest party in the ruling coalition to become CM, it is politically possible, though less likely, for an MLA from a smaller party to become CM if their party is a crucial part of a majority coalition and this is agreed upon in coalition talks. Based purely on the seat data, we cannot definitively say this is impossible. It does not necessarily "must be incorrect" based solely on the seat count. The other options are based on direct numerical sums forming a majority.

Conclusion: Identifying the Incorrect Statement

We are looking for the statement that must be INCORRECT based on the provided election data. Based on our analysis:

• Statement 1 is TRUE.
• Statement 2 is TRUE.
• Statement 3 is FALSE.
• Statement 4 is not necessarily incorrect based purely on the numbers for majority formation.

Therefore, the statement that must be INCORRECT is Statement 3.