Question

Which of the following statements is the negation of “If I become a teacher, then I will open a school”?
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

Hint: We need to break the given condition or statement into two parts, hypothesis, and conclusion. We are trying to find the negation of the statement. So, we take the affirmative sense of the hypothesis and the negative sense of the conclusion. At last, we put two parts together to form the negation.

Complete step-by-step solution:
To form the negation of the conditional statement, we need to take the negation of the conclusion.
So, the form of the statement should be in the form ‘If p, then q’. The mathematical representation of the statement is $p\Rightarrow q$
The negation form of these statements is ‘p and not q’. Its mathematical representation is $p\And \left( \sim q \right)$.
Here we can easily understand the two parts of the statement.
The ‘p’ is the hypothesis part which starts with an ‘if’.
The ‘q’ is the conclusion part which starts with a ‘then’.
So, the inverse of ‘If p, then q’ will be ‘p and not q’.
For our statement “If I become a teacher, then I will open a school”, the ‘If I become a teacher’ part is the hypothesis part which we define as ‘p’ and ‘then I will open a school’ part is the conclusion part which we define as ‘q’.
The affirmative sense of ‘p’ becomes ‘I will become a teacher’.
The negation of ‘q’ becomes ‘I will not open a school’.
Now, we put them together to find the final statement.
The final statement is “I will become a teacher and I will not open a school”. So, (A) is the correct option.

Note: We need to remember that when we are solving the negation form of a statement, we are changing the meaning of the statement. Changing of the form which bears the opposite meaning to the main statement. The inverse formula is independent of whether the parts of the statement are in a negative or affirmative sense. The only thing we need to do is to negate the second part. We need to find the negation form of the conclusion part as they don’t cancel out each other to maintain the opposite meaning of the original statement.