Question

The conjunction of statement: “Mumbai is a city, it is not the capital city.”
A) Mumbai is a city if and only if it is not the capital city.
B) Mumbai is a city if it is not the capital city.
C) Mumbai is a city and it is not the capital city.
D) Mumbai is a city or it is not the capital city.

Answer 1

We will use the definition of conjunction and then find the conjunction of the given statement. Conjunction is a type of logical connectives. Logical connectives are used in mathematics to find the logic between two statements.

Complete step by step solution:
We have logical connectives in mathematics to solve the problem. The logical connectives include Negation, conjunction, disjunction, implication and equivalence.
Here, we need to find the conjunction of the given statement.
The conjunction of a statement is a statement when two statements are joined together by a connector “and”.
So, we can write Mumbai is a city and is not the capital city.
Therefore, the conjunction of the statement “Mumbai is a city, it is not the capital city.” is Mumbai is a city and it is not the capital city.

Thus Option (C) is the correct answer.

Note:
The conjunction of a statement can also be found if both the combining statements are true then the conjunction of the statement is also true. If one or both the statements are false, then the conjunction of the statement is false. This logic is similar to AND logic gate. The conjunction can be denoted by the symbol $\wedge$. For example, if a and b are two statements, then the conjunction of a statement is represented by $p \wedge q$. The logical connector is ‘and’.