Can I sense death?

In the past on more than one occasion, I've sort of been able to 'predict' or 'sense' death of people or close animals to me in my family. Here are the three examples:

1) When I was younger my grandad died (I think it might have been from a heart attack, I can't quite remember). I believe he went out for tea one night with his family, (wife and sort of adopted son I guess, its a long story so I wont go into that) and I think he had a heart attack and died. The same night, I had a nightmare about someone in my family dying, but i didn't know who it was. I woke up in the morning to see my mum crying and she told me the news.

2) Ever since I was little, I've always been really close to one animal in our family. It was my grandma's dog, Gemma. I loved her as much as I do any other member of my family. I had a dream one night where I saw Gemma fall over on the floor and die. For some reason, I knew in the dream she wasn't dead but was going to die. It was later that week she was put down because she couldn't walk (she had athuritus, not sure how its spelt, in her back and joints for a long time and it gradually got worse).

3) My cousin by law (she was married to one of my cousins) had breast cancer for a long time and went through a lot of kemo-therapy (sorry if that's spelt wrong). Thursday morning (yes, last thursday) I woke up with really bad stomach pains, totally out of the blue (it wasn't my time of the month before anyone thinks that so its not cramps) and I was feeling sick and just basically was very ill. I needed to go into school because I had lots of work to do so I told my mum I'd wait and see how I felt. The strange thing was, pretty soon all the pains and sick feelings went away (I hadn't had any pain killers or anything). That evening we got a phone call from my grandma and she told us my cousin in law had died from the breast cancer.

I don't know if these are all just coinsidences because the chances are they could be. One thing is, those are the only people or animals I am very very close to which have died in my family so I wonder if I was predicting/sensing them?

Please let me know what you think.