Dog and cats as pets

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Dog and cats are intelligent animals. I say this because I have a pet dog who can do a lot of tricks. I know it is not uncommon as dogs can be trained, taught some tricks and are loyal pets, thus they are "man's best friend". But what concerns me is my cat. With the love and care I showered on her, feeding her to her heart's content, she gave back my kindness by keeping the house rodent free, doesn't steal food from the table or anywhere but just wait until food is given her. She always goes to the same spot I assign for her to pee. One time when she was pregnant and about to delivery her kittens, she gave a weird cry as if telling me to open the door to my bedroom which I did and there she gave birth to 2 lovely kittens. And there had been so many instances that she could almost always understand what I want her to do or to go as if we speak the same language. Is you cat like this?