Worksheets — Set 6

Discrete math · Relations, recurrences, and graphs

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

Warm-up

1. How many subsets does a set with 10 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 9 fair tosses) = ___

_See printable PDF for diagram._

Written practice

1. How many subsets does a set with 9 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 8 fair tosses) = ___ 4. Write the recurrence aₙ = 8aₙ₋₁ with a₀ = 1 ___ 5. Graph with 10 vertices — minimum edges for connectivity? ___ 6. Convert 48₁₀ to base 9. = ___ 7. How many subsets does a set with 12 elements have? ___ 8. P(at least one head in 11 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 11aₙ₋₁ with a₀ = 1 ___ 2. Graph with 13 vertices — minimum edges for connectivity? ___ 3. Convert 51₁₀ to base 12. = ___ 4. How many subsets does a set with 15 elements have? ___ 5. P(at least one head in 14 fair tosses) = ___ 6. Write the recurrence aₙ = 14aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 26 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 25 fair tosses) = ___

_See printable PDF for diagram._

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Parent tip: Use trees or tables for counting