Symbolize the following sentences.

1.  Alice likes Ted but she does not like Carol.
    Lat & ~Lac

2.  Everyone likes Alice.
    (x)Lxa

3.  Alice likes everyone.
    (x)Lax

4.  Some individuals like everyone.
    (Ex)(y)Lxy

5.  There are individuals who do not like anyone.
    (Ex)(y)~Lxy