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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 Mathematicsa) Let A = B = \{x | -1 \leq x \leq 1\} for each of the following functions state where it is injective, surjective or bijective i) g(x) = \sin \pi x ii) h(x) = \frac{2x}{3}20237mDiscrete MathematicsUse Cantor's diagonal argument to prove that set F of all functions f: (0,1) \rightarrow R has larger Cardinality than |R|.20237m
Previousa.) find the power set of each of these sets i) \{a, b\} ii) \{\emptyset, \{\emptyset\}\}NextProve the following by using the principle of mathematical induction for all n \in N: 1^3 + 2^3 + 3^3 + \dots + n^3 = \left(\frac{n(n+1)}{2}\right)^2
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