If adenocarcinoma is in women or without a tumor, then adenocarcinoma is without a tumor and a non-breast cancer.
Either in women or in men.  No men have breast cancer. Either breast cancer or non-breast cancer.  No type of cancer is without a tumor. All non-breast cancers are a type of cancer. If adenocarcinoma is a type of cancer or without a tumor, then adenocarcinoma is in women or without a tumor.
∀x (Women(x) ∨ Men(x))   ∀x (Men(x) → ¬BreastCancer(x))  ∀x (BreastCancer (x) ∨ Non-BreastCancer(x))   ∀x (ATypeOfCancer(x) → ¬WithoutTumor (x))   ∀x (Non-BreastCancer(x) → ATypeOfCancer(x))   ATypeOfCancer(adenocarcinoma) ∨ WithoutTumor(adenocarcinoma) → women(adenocarcinoma) ∨ WithoutTumor(adenocarcinoma)