Select the ordered pair of statements which are logically consistent with the main statement.
Main Statement:
Whenever Sakshi hears it’s someone's birthday, she orders a cake.
A. Sakshi heard of someone's birthday.
B. Sakshi did not hear of someone's birthday.
C. Sakshi ordered a cake.
D. Sakshi did not order a cake.

Correct option is B

Given:
Whenever Sakshi hears it’s someone's birthday, she orders a cake.
Solution:
From main statement, we can conclude:
If Sakshi hears about a birthday, then she must order a cake.
If she did not order a cake, it means she did not hear about a birthday.
AB:
A: Sakshi heard of someone's birthday.
B: Sakshi did not hear of someone's birthday.
These two statements are contradictory (she can't both hear and not hear about a birthday), so this option is not consistent.
DB:
D: Sakshi did not order a cake.
B: Sakshi did not hear of someone's birthday.
This pair is consistent. If Sakshi did not hear of a birthday, she would not order a cake. So, this option is consistent with the main statement.
CA:
C: Sakshi ordered a cake.
A: Sakshi heard of someone's birthday.
While this pair might seem consistent at first, it actually does not logically follow from the main statement. The main statement only states that hearing of a birthday will lead to ordering a cake, but it does not imply the reverse (i.e., ordering a cake does not guarantee that she heard about a birthday). Therefore, this option is not necessarily consistent.
BD:
B: Sakshi did not hear of someone's birthday.
D: Sakshi did not order a cake.
This pair is consistent, as not hearing about a birthday would mean she did not order a cake. However, this is essentially the same as option (b) and does not add a new pair.
The only logically consistent pair, based strictly on the main statement, is:
- DB
Note- The options "AB" and "DB" are not the same. This is because in the direction of the question it is mentioned that the options are ordered pairs.