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 son of P?

Option 1: P × R – Q

Option 2: P + Q – R

Option 3: P – R × Q

Option 4: P – Q + 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.

Now, let's check the options –
First option: P × R – Q
According to the given information, the family tree will be –

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 niece or nephew of P.
Second option: P + Q – R
According to the given information, the family tree will be –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it's clear that Q is the daughter of P.
Third option: P – R × Q
According to the given information, the family tree will be –

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 son or daughter of P.
Fourth option: P – Q + R
According to the given information, the family tree will be –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure. From the above family tree, it's clear that Q is the son of P.

So, only the fourth option fulfils the relation as per the family tree. Hence, the fourth option is correct.