Use element argument to prove the statement. Assume that all sets are subsets of a universal set U, Statement: For all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C), I have atteched the example to...

Use element argument to prove the statement. Assume that all sets are subsets of a universal set U, Statement: For all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C), I have atteched the example to use to solve this problem. Please help me becuase I could not figure it out.

Extracted text: 10. For all sets A, B, and C, (AU B) NC S AU(BNC). Prnf: Let 4.B¢ C be Let xEAue) C. Then xe AUB ard rE c 2 KE A or xeB) ad xeC, If xe A , Hen xe AulBnc) If xEB, ten xG BnC > xe AulBnc). sefs, 14. For all sets A and B, AU (AN B) = A. nof Let 4a 6 be any sets. AUCANB) E A : Led xe AUCANB). by dehndan ofencón, XEA or xEA and xE B. Sggoe A. Then xe A and xeB So xE A AE AULANB): Let xE A. Hen xE A OCANB) by detnchon unin. 19. For all sets A, B, and C, if A C B and A C C then A C BnC. Prut: Let 4, baC be set o any AEB & AEC. Let xeA. Then xEB CÁC B) and xeC CAEB). So, x c BnC.