Discrete Mathematics

Use this for “If the server is down, the page fails. The page fails. So the server is down. Is this valid?”

Use this for “Is ¬q → ¬p equivalent to p → q? Build the truth table.”

Use this for “Prove that 1 + 2 + … + n = n(n + 1) ÷ 2 for every n ≥ 1.”

Use this for “A has 3 elements and B has 4. How many subsets does A have, and how many ordered pairs are in A × B?”

Use this for “How many functions are there from a 3-element set to a 4-element set, and how many of them are one-to-one?”

Use this for “Is f(n) = 2n from ℤ to ℤ one-to-one, onto, both or neither?”

Use this for “In how many ways can 10 identical balls go into 4 boxes? With at least one in each box?”

Use this for “Among 50 people, at least how many share a birth month? How many people force 5 in one month?”

Use this for “4 letters go into their 4 envelopes at random. In how many ways does no letter reach its own envelope?”

Use this for “How many different words can be made from all 11 letters of MISSISSIPPI?”

Use this for “A full 3-ary tree has 4 internal vertices. How many vertices, leaves and edges?”

Use this for “How many edges has K₇? How many has the complete bipartite graph K₃,₄?”

Use this for “A connected graph has degrees 3, 3, 2, 2. Does it have an Euler path or an Euler circuit?”

Use this for “Tower of Hanoi: a₁ = 1 and aₙ = 2aₙ₋₁ + 1. How many moves for 10 disks?”

Use this for “Solve aₙ = 4aₙ₋₁ − 4aₙ₋₂ with a₀ = 1, a₁ = 4.”