Question

The dual of the statement,”Ram and Laxman are brothers”, is
A. Ram or Laxman are brothers.
B. Ram and Laxman are not brothers.
C. Ram and Laxman are brothers.
D. Laxman or Ram are brothers.

Answer 1

Hint:
If the statement has an $and$ in it then in the dual of the same statement the $and$ is replaced with an $or$ . In the given statement,”Ram and Laxman are brothers”, there is an $and$ so replace it with an $or$ to get the statement’s dual.

Complete step by step solution:
We are given a statement, “Ram and Laxman are brothers”.
We have to find the dual of the given statement.
Let us consider an expression p Ʌ q, where $ Ʌ $ represents $and$ . This expression has and in it. So in the dual, the $and$ must be replaced with an $or$. Therefore, the dual expression is p V q, where V represents $or$.
In the same way, the statement “Ram and Laxman are brothers” has an $and$ so to get the dual statement we just have to replace $and$ with $or$.
Therefore, the dual of the given statement is “Ram or Laxman are brothers”.
The correct option is Option A, Ram or Laxman are brothers.

Additional Information:
If the compound statements are combined using the word ‘and’ then the resulting statement is called conjunction. If the compound statements are combined using the word ‘or’ then the resulting statement is called disjunction.

Note:
The duality can be applied only for compound statements and compound statements are obtained by joining two or more simple statements using ‘and’ or ‘or’. Dual of a conjunction is disjunction and dual of a disjunction is conjunction.