Worksheets — Set 19

Discrete math · Logic and proof

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

Warm-up

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._

Written practice

1. How many subsets does a set with 22 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 21 fair tosses) = ___ 4. Write the recurrence aₙ = 21aₙ₋₁ with a₀ = 1 ___ 5. Graph with 23 vertices — minimum edges for connectivity? ___ 6. Convert 61₁₀ to base 22. = ___ 7. How many subsets does a set with 25 elements have? ___ 8. P(at least one head in 24 fair tosses) = ___

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More written practice

1. Write the recurrence aₙ = 24aₙ₋₁ with a₀ = 1 ___ 2. Graph with 26 vertices — minimum edges for connectivity? ___ 3. Convert 64₁₀ to base 25. = ___ 4. How many subsets does a set with 28 elements have? ___ 5. P(at least one head in 27 fair tosses) = ___ 6. Write the recurrence aₙ = 27aₙ₋₁ with a₀ = 1 ___

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Patterns and rules

1. How many subsets does a set with 39 elements have? ___ 2. Prove or disprove: if n is even, n² is even. 3. P(at least one head in 38 fair tosses) = ___

_See printable PDF for diagram._

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Stretch

1. How many subsets does a set with 47 elements have? ___ 2. Prove or disprove: if n is even, n² is even.

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Parent tip: Use trees or tables for counting