Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

A murder has been committed in a house. You are a detective and have to find out the murderer.

You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.

There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.

Can you identify the murderer and the four liars? Also, can you find out who was in which room?

The responses of all the suspects are mentioned below.

Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.

David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

The following "Brain Bat" means Slow Down.
S
L
O
W

Using the same logic, can you tell us what does the following Brain Bat means ?
E
V
I
G

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?

John asked Jack, "The time right now is 7 pm. Can you tell me what will be the time 23, 999, 995 hours later ?"

While Bella does not know the answer, do you ?

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?