Write each of the following in symbolic form using p Sybil

Write each of the following in symbolic form using p = \"Sybil does not play basketball\", q = \"Sybil likes singing\", r = \"Sybil wants to take up a career in singing\" Sybil plays basketball and it is not the case that she likes singing. Sybil wants to take up a career in singing if and only if she likes singing. If Sybil does not play basketball, then she does not like singing. If Sybil likes singing and she wants to take up a career in singing, then she plays basketball. If Sybil likes singing, then she wants to take up a career in singing but she plays basketball.

Solution

Symbolic forms :

1) ~p ^ ~q

2)(q <-> p)

3)p -> ~q

4) (q ^ r) --> ~p

5) q --> (r ^ ~p)