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- For the sets gives in Exercise 9, is there a distributive relationship for union with respect with respect in intersection? That is does ABC=ABAC? A=1,2,3,4, B=2,4,6,8, and C=1,3,5,7,9.7. For the given subsets and of Z, let and determine whether is onto and whether it is one-to-one. Justify all negative answers. a. b. c. d.For the given subsets A and B of Z, let f(x)=2x and determine whether f:AB is onto and whether it is one-to-one. Justify all negative answers. a. A=Z+,B=Z b. A=Z+,B=Z+E
- 6. For the given subsets and of Z, let and determine whether is onto and whether it is one-to-one. Justify all negative answers. a. b.Label each of the following statements as either true or false. Let f:AB. Then f(A)=B for all nonempty sets A and B.For each of the following relations R defined on the set A of all triangles in a plane, determine whether R is reflexive, symmetric, or transitive. Justify your answers. a. aRb if and only if a is similar to b. b. aRb if and only if a is congruent to b.
- True or false Label each of the following statement as either true or false. Let and , then .Label each of the following statements as either true or false. 2. for all nonempty sets A and B.For the sets given in Exercise 9, is there a distributive relationship for intersection with respect to union? That is, does ABC=ABAC? A=1,2,3,4, B=2,4,6,8, and C=1,3,5,7,9.
- [Type here] 7. Let be the set of all ordered pairs of integers and . Equality, addition, and multiplication are defined as follows: if and only if and in , Given that is a ring, determine whether is commutative and whether has a unity. Justify your decisions. [Type here]Prove that if m0 and (a,b) exists, then (ma,mb)=m(a,b).
