14122. (The late “Lewis Carroll.”)—It is given that (1), if C is true, then, if A is true, B is not true; and (2), if A is true, B is true. Can C be true? What difference in meaning, if any, exists between the following propositions?—(1) A, B, C cannot be all true at once; (2) if C and A are true, B is not true; (3) if C is true, then, if A is true, B is not true.