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Show that the sets
5. Determine, for each of the following sets, whether or not it is countable. Justify your answers.
(a) The set
(b) The set
(c) The set
(d) The set
(e) The set
(f) The set
(g) The set
(h) The set
(i) The set
(j) The set
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Topology
- 21. A relation on a nonempty set is called irreflexive if for all. Which of the relations in Exercise 2 are irreflexive? 2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric, or transitive. Justify your answers. a. if and only if b. if and only if c. if and only if for some in . d. if and only if e. if and only if f. if and only if g. if and only if h. if and only if i. if and only if j. if and only if. k. if and only if.arrow_forward13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.arrow_forwardIn each of the following parts, a relation R is defined on the power set (A) of the nonempty set A. Determine in each case whether R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if xy. b. xRy if and only if xy.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,