Question

Write negation of –
If I eat healthy then I will not fall ill.
A.If I will not eat healthy then I will not fall ill.
B.If I will eat healthy then I will fall ill.
C.I eat healthy but I will fall ill.
D.I eat healthy or I will not fall ill.

Answer 1

Hint: The statement given here is a conditional statement which is in form ‘if p then q’. The negation of a statement has the opposite meaning of the original statement and it is represented by the symbol $ \sim $ .

Complete step-by-step answer:
The given statement is-
If I eat healthy then I will not fall ill.
Let ‘I eat healthy’ be statement p and ‘I will not fall ill’ be the statement q.
Then the statement becomes of the form -‘if p then q’
This type of statement is called a conditional statement. And we have to find the negation of this statement. Consider, if the statement is p then the negation is represented by $ \sim p$ .
Here the statement can also be written in the form of $p \to q$
On applying negation we get,
$ \Rightarrow \sim \left( {p \to q} \right)$ $ = p \wedge \sim q$
Because the negation of conditional statement is given as-\[ \sim \left( {p \to q} \right) = p \wedge \sim q\]
Then this means the p statement will remain the same but the negation will be applied to the q statement. If and then are removed from the statement. Here $ \wedge $ sign means ‘but’.
So the $ \sim q$ statement will be ‘I will fall ill’.
Then the negation of the statement will be-
‘I eat healthy but I will fall ill’
Hence the correct answer is C.

Note: The student may get confused as to why the ‘not’ word was removed from statement q in the answer.Here in the statement q there was already a negation ‘not’ present in it and we know that-
$ \Rightarrow \sim \left( { \sim q} \right) = q$
Hence the ‘not’ was removed from the statement q when negation was applied.