2.2.33 Rewrite this statement as a conjunction of two if-then statements: This integer is even if, and only if, it equals twice some integer. 2.2.43 Use the contrapositive to rewrite this statement in if-then form in two ways: Doing homework regularly is a necessary condition for Jim to pass the course. Use symbols to write the logical form of these arguments. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made: 2.3.29 If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6. Neither of these two numbers is divisible by 6. The product of these two numbers is not divisible by 6. 2.3.32 If I get a Christmas bonus, Ill buy a stereo. If I sell my motorcycle, Ill buy a stereo. If I get a Christmas bonus or I sell my motorcycle, then Ill buy a stereo.