Question

The negation of the statement: “If I become a teacher, then I will open a school”, is

• A. I will become a teacher and I will not open a school
• B. Either I will not become a teacher or I will not open a school
• C. Neither I will become a teacher nor I will open a school
• D. I will not become a teacher or I will open a school

Answer 1

The correct option is A

I will become a teacher and I will not open a school

Explanation for the correct answer:

Let $p$ denote the statement that ‘I will become a teacher’

Let $q$ denote the statement that ‘I will open a school’

The given statement is that, ‘If I become a teacher, then I will open a school’

This statement can be written in Boolean format as $p\to q$

The negation of this statement can be written as,

$~\left(p\to q\right)\equiv p\wedge ~q$

This statement can be written in word format again as,

‘I will become a teacher and I will not open a school’

Hence, option $\left(A\right)$ is the correct answer.