Discrete Mathematics - Solutions Manual|QUESTIONS WITH 100% CORRECT & VERIFIED ANSWERS. LATEST UPDATE
Chapter 1 Sets and Logic 1.1 Exercises with solutions (1.1) Determine the cardinality of the following sets. (a) {∅} The set {∅} contains exactly one element, which is the empty set ∅. Therefore, the cardinality is: ∣{∅}∣ = 1. (b) {{∅}} This set contains exactly one element, which is the set {∅}. Therefore, the cardinality is: ∣{{∅}}∣ = 1. (c) {{∅},∅} This set contains two distinct elements: {∅} and ∅. Therefore, the cardinality is: ∣{{∅},∅}∣ = 2. (d) {∅, {∅},∅} Even though ∅ is repeated, a set only contains unique elements. Therefore, this set still has two distinct elements: ∅ and {∅}. The cardinality is: ∣{∅, {∅},∅}∣ = 2. (e) {∅, {∅}, {{∅},∅}, {∅}} 6 The set contains three distinct elements: ∅, {∅}, and {{∅},∅}. Although {∅} is repeated, the cardinality of this set is:
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discrete mathematics
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for each of the sets
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discrete mathematics solution manual
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anthony bonato discrete mathematics
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determine the cardinality of the following sets
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let a 1 2 3 b 3 4 5 and u 1 2 3
