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Discrete MathematicsWhich of the following two sets are equal? (i) A = \{1, 2\} and B = \{1\} (ii) A = \{1, 2\} and B = \{1, 2, 3\} (iii) A = \{1, 2, 3\} and B = \{2, 1, 3\} (iv) A = \{1, 2, 4\} and B = \{1, 2, 3\}20222mDiscrete Mathematicsa.) find the power set of each of these sets i) \{a, b\} ii) \{\emptyset, \{\emptyset\}\}20237mDiscrete MathematicsDetermine if the sets are countable or uncountable a.) the set A of all function g: Z_+ \rightarrow Z_+ b.) The set B of all functions f: Z_+ \rightarrow \{0,1\}202314mDiscrete Mathematics(b) Indicate which of the following statements are true and which are false. Justify your answers as best you can: (i) \forall x \in \mathbf{Z}^+, \exists y \in \mathbf{Z}^+ such that x = y+1 (ii) \forall x \in \mathbf{Z}, \exists y \in \mathbf{Z} such that x = y+1 (iii) \exists x \in \mathbf{R} such that \forall y \in \mathbf{R}, x = y+1 (iv) \forall x \in \mathbf{R}^+, \exists y \in \mathbf{R}^+ such that xy = 1 (v) \forall x \in \mathbf{R}, \exists y \in \mathbf{R} such that xy = 1 (vi) \forall x \in \mathbf{Z}^+ \text{ and } \forall y \in \mathbf{Z}^+, \exists z \in \mathbf{Z}^+ \text{ such that } z = x-y (vii) \forall x \in \mathbf{Z} \text{ and } \forall y \in \mathbf{Z}, \exists z \in \mathbf{Z} \text{ such that } z = x-y (viii) \exists u \in \mathbf{R}^+ \text{ such that } \forall v \in \mathbf{R}^+, uv < v20228m
PreviousLet N = \{1,2,3,......\} be ordered by divisibility, which of the following subset is totally ordered (i) \{2, 6, 24\} (ii) \{3, 5, 15\} (iii) \{2, 9, 16\} (iv) \{4, 15, 30\}NextUse Cantor's diagonal argument to prove that set F of all functions f: (0,1) \rightarrow R has larger Cardinality than |R|.