Question

Write dual of statements:
Rushil and Rushita can speak Sanskrit.
A. Rushil and Rushita cannot speak Sanskrit.
B. Rushil or Rushita can speak Sanskrit.
C. Rushil or Rushita cannot speak Sanskrit.
D. Rushil and Rushita can speak other than Sanskrit.

Answer 1

Hint:- Dual statements means that we had to replace $\wedge$ (Logical AND) with $\vee$ (Logical OR) and replace or with AND.

Complete step-by-step solution -
Dual statement is just the negation of the given statement or in other words we can say that if any statement is true then its dual will be false or if the statement is false then its dual will be true.
So, there can be many types of dual statements.
And they can also be meaningful or meaningless.
Like if there is a statement that “two is less than three” then its dual must be “two is greater than three” knowingly that it will be an impossible statement because 2 is always less than 3.
As we know that we are given the statement that “Rushil and Rushita can speak Sanskrit”.
So, to find the dual of this statement we had to just replace “and” with “or” and “can” with “cannot”.
So, the dual off the statement “Rushil and Rushita can speak Sanskrit” will be “Rushil or Rushita cannot speak Sanskrit”
Hence, the correct option will be C.

Note:- Whenever we come up with this type of problem then we had to only find the negation of the given statement and negation of any statement is only the opposite of the given statement in terms of meaning. So, if the sentence is saying that it is true then we can use it not to make the sentence false. This will be the easiest and efficient way to find the solution of the problem.