Question

Consider the following statements
$p:$ Virat Kohli plays cricket
 $q:$ Virat Kohli is good at Mathematics
 $r:$ Virat Kohli is successful.
Then negation of the statement “if Virat Kohli plays cricket and is not good at Mathematics then he is successful “will be:
(A) $\sim p \wedge (q \wedge r)$
(B)$(\sim p \vee q) \wedge r$
(C) $
  p \wedge (\sim q \wedge \sim r) \\
    \\
 $
(D) None of these

Answer 1

Hint: We know that we have different symbols for trueness and falsehood of statement and for connectivity of statements and to write negation.
Negation means the opposite of the given statement; it is generally denial of some words or statement.
We will use such symbols to find negation.

Complete step-by-step answer:
We are given statements as follows-
Statement $p$ says Virat Kohli plays cricket
Statement $q$ conveys Virat Kohli is good at Mathematics
Statement $r$ implies Virat Kohli is very successful
We have to find negation “if Virat Kohli plays cricket and is not good at Mathematics then he is successful “
So we will break this statement in four parts
 First part if Virat Kohli plays cricket this is statement p
Next is and so symbol of and is ^
Third part – is not good at Mathematics this is negation of statement q $( \vee q)$
Fourth part then he is successful $\left( { \vee r} \right)$ this is a true statement
Now combining all four parts we have our statement as $(p \wedge \vee q) \vee r$
Now, we have to find negation of this statement $(p \wedge \vee q) \vee r$
It will be, $\sim (p \wedge \sim q) \vee r$ and $\sim p \wedge = p \vee $
In words negation of or is and
On solving this negation
$\sim p \vee \sim (\sim q)) \wedge \sim r$
We know that $\sim (\sim q) = q$
Simplifying more
$(\sim p \vee q) \wedge \sim r$ .
Therefore our answer is $(\sim p \vee q) \wedge \sim r$

So, the correct option is (d) none of these

Note: Read question very carefully; always remember all of the points mentioned below-
Make sure that you don’t get confused in the symbol of and, or as well as their negations.
Negation of negation of any statement is the statement itself.
Negation of and is or.