Unit 11 Answers

1. a) {-2, 2}      b) emptyset.gif (909 bytes)

2. a) Yes        b) No        c) No

3. a) No     b) Yes     c) Yes      d) No      e) No      f) No

4. Let x be an arbitrary element of A.  We are going to show that x in.gif (889 bytes) C.  Since A subseteq.gif (874 bytes) B, this implies that xin.gif (889 bytes) B.  SinceB subseteq.gif (874 bytes) C, we see that x in.gif (889 bytes) C.  Since x in.gif (889 bytes)A implies that x in.gif 
(889 bytes) C, it follows that A subseteq.gif (874 bytes) C.

5.

  1. {emptyset.gif (909 bytes), {a}}
  2. {emptyset.gif (909 bytes), {a}, {{a}}, {a, {a}} }
  3. {emptyset.gif (909 bytes), {emptyset.gif (909 bytes)}, {{emptyset.gif (909 bytes)}}, {emptyset.gif (909 bytes), {emptyset.gif (909 bytes)}}}