Question

DISCRETE/LOGIC MATH

please show work and explain

3. Let A, B, C be sets. Use the Venn Diagram below to help give a counterexample to the statements in parts (a) and (b). In each case, if the Venn diagram suggests a relationship between the LHS and RHS (without any additional hypotheses), then state and prove it. с (a) For all sets A,B,C, (A (b) For all sets A, B, C, ( A B B C = A ( B C = A C ). (BCC). )

Answer 1

Here, A-B ANB for all getę A,B,C. CA1B) 10=AI (BIC) Now (A1B) Here the given wen diagramm Bet 't' contains 1, 2, 5, 6 And Bet i contain & 2, 3, 4,5. At q{1,2,5,6) and Bs [ 22,3,4,5) AlB is the remove the elements of set B from A Bolo #18 - 21,6% Now CAIB) 1 c = ? Remove the elements of B nc from AB Anc AlB

shaded part is - CAIB) ac Thus CAIB) Ical LHS And Now, RHS first we calculate Colc) Вас B2 А В Then ble - $ 2,33 Now al Coley remove (Ble) from A Since the already remove d elementa forom 'B' So, we have Ble= {2,3} After removing ble from A ie; fl (B\C)= 14

It Al CB\c)= {i} doesn't contain 6 when we calculate Al CBIC). It excludes all the clements of 'c? In this past, - I didn't understand what is that Symbol 6. So, I hoole it as 'U' Cunion ) CAUBC) uc = AU CB Cuc) (b) CHE se a $1,6,7,8} 1 Remove B from AB A= {1,4, 5,6% SO, AUB= { 1,2,5,6,7,8 ] and coo$ 4,5,6,73 gb, CAUB) CUC = { 1,2,5,6,7,840x 4,5,6,7% CAUBJUe =118, 4, 5, 6, 7,8%

PHR Bruc = {1, 6, 7, 8} {4, 5, 6, 29 = { 1,4,5,6,7,8} Now AU (Buc) = {1, 2,5,6} {1,4,5,6,7,8} s 112,4,5,6,7,8 % = CA UBC) uc = AUCB cuc) (HS = RHS * Please "prote" if it's Helpful, -Thank you *