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

Hint: In mathematical logic, conjunction is used for connecting simple statements to form compound statements using the connector ‘and’. So we can connect the statements using and.

Complete step-by-step answer:
In mathematics, conjunction of two statements means connecting two simple statements using a connector. Conjunction is denoted by ‘ ^ ’ and the connector is usually AND. If p and q are two statements, conjunction of p and q is denoted by p ^ q. p ^ q is true only when both p and q are true.
In our question, 2 statements are given, we can take
p – Mumbai is a city
q – it is not the capital city
The conjunction of p and q is
p ^ q – Mumbai is a city and it is not the capital city.
Therefore, the correct solution is option C.

Note: Conjunction of two statements is true only when both the statements are true. The conjunction is false if either p or q is false. It is similar to the logic gate AND. We can draw a truth table to know how p and q affects the conjunction p ^ q.