Assuming your table of data is called ProjectInfo:
SELECT DISTINCT Contract, Activity
FROM ProjectInfo
WHERE Contract = (SELECT Contract
FROM (SELECT DISTINCT Contract, Activity
FROM ProjectInfo) AS ContractActivities
GROUP BY Contract
HAVING COUNT(*) = 1);
The innermost query identifies the contracts and the activities. The next level of the query (the middle one) identifies the contracts where there is just one activity. The outermost query then pulls the contract and activity from the ProjectInfo table for the contracts that have a single activity.
Tested using IBM Informix Dynamic Server 11.50 - should work elsewhere too.