Question : Directions: If A – B means that A is the father of B, A + B means that A is the mother of B, and A × B means that A is the brother of B, then which of the following expressions shows that Q is the brother of P?

Option 1: P × Q – R

Option 2: P × Q + R

Option 3: R + P × Q

Option 4: Q – P × R

Correct Answer: P × Q – R

Solution : Given:
A – B means that A is the father of B.
A + B means that A is the mother of B.
A × B means that A is the brother of B.

Let's check the given options –
First option: P × Q – R
According to the given expression, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it is evident that Q is the brother of P.
Second option: P × Q + R
According to the given expression, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it is evident that Q is the sister of P.
Third option: R + P × Q
According to the given expression, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it is evident that the gender of Q is undefined. Q can either be the sister or brother of P.
Fourth option: Q – P × R
According to the given expression, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it is evident that Q is the father of P.

So, only the expression in the first option satisfies the relation given in the question. Hence, the first option is correct.