Which of the following statements is biconditional?
i am sleeping if and only if i am snoring.
mary will eat pudding today if and only if it is custard.
it is raining if and only if it is cloudy.
none of the above.
why is the answer none of the above?

Answer with Step-by-step explanation:

We are given some statements

We have to find that which statements is bi-conditional

We know that

Bi-Conditional statement:It is combination of conditional statement and its converse written as  if and only if .Bi- conditional statement is true if and only both the conditions are true.

1.I am sleeping if and only if I am snoring.

If I am sleeping then I am snoring .Then,it may be true or may not be  true.

If I am snoring then I am sleeping .It is true.

Its one side true result.So, it is not bi conditional true statement.

2.Mary will eat pudding today if and only if is custard.

If Mary will eat pudding today then it is custard.It may or may not be true because pudding can be any soft sweet desserts.It is not necessary that it is custard only.

If it is custard then Mary will east pudding today.It is true, because it is soft sweet dessert.

Hence, it is one side true. Therefore, It is not bi- conditional true.

3.It is raining if and only if it is cloudy.

If it is raining then it is cloudy .It is true.

But if it is cloudy then it is raining. It  may be true or may not be true.

Hence, it is one side true result.Therefore, it is not bi conditional true.

Therefore, any given statement is not both side true.

So, the answer is none of the above because bi conditional statement is true if and only if both the conditions are true.

d. is the correct answer

step-by-step explanation: