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Draw hasse diagram representing the positive divisor of 36 and show digraph to It?
Let A = {a,b,c,d}, B = {1,2,3}, and R = {(a,2), (b, 1), (c, 2), (d, 1)}.
(a)Is R a function?
(b)Is R−1 a function?
Explain your answers.
Let A = {1,2,3,4,5,6} and let p1 = (3,6,2) and p2 = (5, 1, 4) be permutations of A.
(a) Compute p1 ◦ p2 and write the result as a product of cycles and as the product of
transpositions.
(b) Compute p−1 ◦ p−1
The market for lemon has 10 potential consumers, each having an individual demand curve
P = 101 - 10Qi
, where P is price in dollars per cup and Qi is the number of cups demanded
per week by the i
th consumer. Find the market demand curve using algebra. Draw an
individual demand curve and the market demand curve. What is the quantity demanded by
each consumer and in the market as a whole when lemon is priced at P = $1/cup?
Let A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15} and define relations R and S from X to Y as
follows:
for all (x,y) ∈A × B, x R y ⇔ y % x
for all (x,y) ∈A × B, x S y ⇔ (y – 4)+2 = x
State explicitly which ordered pairs are in A × B, R, S and type of relation
Let A={0, 1,2}×{2, 5,8}={(0, 2), (0, 5), (0, 8), (1, 2), (1, 5), (1, 8), (2, 2), (2, 5), (2, 8) }.
A partial order relation R on A is defined by (a, b) R(c, d) if and only if (a+b) divides (c+d). Draw a hasse diagram for poset A.
State the converse and contrapositive of each of the following implications.
(a) If it does not rain tonight, I will go fishing tomorrow.
(b) If it rains tonight, then I will stay at home.
solve the recurrence t(n)=(t(n/2)^2) assuming t(1)=1
Given the following 2 premises, 1. 𝑝 → (𝑞 ∨ 𝑟) 2. 𝑞 → 𝑠 Prove 𝑝 → (𝑟 ∨ 𝑠) is valid using the Proof by Contradiction method.
prove a --> ( b V c ) using contradiction method and combination of inference rules and equivalence laws from these premises : 1. a --> ( d V b ) 2. d --> c
#340153 on Dec 2023