Question : Directions: If R ÷ S means that R is the mother of S, R × S means that R is the father of S and R – S means that R is the sister of S, then which of the following expressions shows that P is the father of R?

Option 1: P × Q ÷ R

Option 2: Q × P – R

Option 3: R × Q – P

Option 4: P × Q – R

Correct Answer: P × Q – R

Solution : Let's check the 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 P is the maternal grandfather of R.
Second 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 P is the sister of R.
Third option: R × Q – P
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 P can either be the daughter or the son of R, as the gender of P is undefined.
Fourth 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 P is the father of R.

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