Worksheets — Set 3

Discrete math · Sets, functions, and counting

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. How many subsets does a set with 7 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 6 fair tosses) = ___

_See printable PDF for diagram._

Written practice

1. How many subsets does a set with 6 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 5 fair tosses) = ___ 4. Write the recurrence aₙ = 5aₙ₋₁ with a₀ = 1 ___ 5. Graph with 7 vertices — minimum edges for connectivity? ___ 6. Convert 45₁₀ to base 6. = ___ 7. How many subsets does a set with 9 elements have? ___ 8. P(at least one head in 8 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 8aₙ₋₁ with a₀ = 1 ___ 2. Graph with 10 vertices — minimum edges for connectivity? ___ 3. Convert 48₁₀ to base 9. = ___ 4. How many subsets does a set with 12 elements have? ___ 5. P(at least one head in 11 fair tosses) = ___ 6. Write the recurrence aₙ = 11aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 23 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 22 fair tosses) = ___

_See printable PDF for diagram._

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Parent tip: Use trees or tables for counting