Solution 3A Peeping with B1 here or at “a” would be simply awful for Black, because the connected White stones are then very strong, while B1 becomes an almost worthless stone plastered against a strong opposing formation. Such moves mainly help the opponent, and so are called “thank you” moves!
Solution 3B Correct is to cut with B1, provided Black has assessed that it will have good prospects in any resulting fight! W2 or W “a” to follow is almost mandatory, but in either case White is separated. What will develop next will depend on other nearby stones of both colors, the full board position, the strength of the players, and their strategy.