2.4. Use Venn diagrams to verify that if A is contained in B, then AnB A...
3. (12') Using Venn diagrams, verify the following identities. (a) A-(AnB)U(A-B) ( b) If A and B are finite sets, we have (AUB)- A+B-(AnB )
2.1. Use Venn diagrams to verify that (a) (A UB)UC is the same event as AU(BUC) (b) An(BUC) is the same event as (AnB)U(AnC); (c) A U (Br C) is the same event as (A U B) (A U C)
2.2. Use Venn diagrams to verify the two De Morgan laws: (b) (AUB) A'n B'.
1. Let A, B and C be events in the sample space S. Use Venn Diagrams to shade the areas representing the following events (32 points) a. AU (ANB) b. (ANB) U ( AB) C. AU ( ANB) d. (AUB) N (AUC)
4. On the following Venn diagrams, use shaded area to represent (a) (An B')UC (b) (A -B)nc. (c) (BUC)n(A'UB). B S
use venn diagrams to show AuB' is equal to A'nB' A = 1 & 2 B = 2 & 3 outlaying area = 4
Exercise 3.9. Draw Venn Diagrams to convince yourself of the following facts: (Thus, AC B An B -ø, ie. they're logically equivalent statements. We could have used either one as a definition of what it means to be a subset!) c Similarly, convince yourself that ACB iff AnB-A (Recall that "iff", " ㈠ ", and "is logically equivalent to" all mean the same thing)
Use Venn diagrams to prove or disprove the following c) AU B (An B) u (A n B)u (A n B) d) A U (B n C) (AU B) n (AU C)
Use membership tables (i.e., no set identities or Venn diagrams)
to demonstrate that
4. Use membership tables (i.e., no set identities or Venn diagrams) to demonstrate that ((Y U Z) n (X UZ)) – (Y nz) and (2 U(Y nx)) ((CY NZ) ux)u((YnZ)n x)) are equivalent expressions. (5 marks)
Exercise 3.9. Dra facts: Venn Diagrams to convince yourself of the following (Thus, A CBAnB , i.e. they're logically equivalent statements. We could have used either one as a definition of what it means to be a subset!) c Similarly, convince yourself that AC Biff AnB A (Recall that "iff", "" same thing) and "is logically equivalent to " all mean the