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If 2 distinguishable dice are rolled, in how many ways can they fall? If 5
distinguishable dice are rolled, how many possible outcomes are there? How
many if 100 distinguishable dice are tossed?
The chairs of an auditorium are to be labeled with a letter and a positive integer
not exceeding 100. What is the largest number of chairs that can be labeled
differently?
Let f : A → B, g : B → C, and h : C → D be functions.
1. State what you need to show to conclude that h ◦ (g ◦ f) = (h ◦ g) ◦ f. 13
2. Consider now some a ∈ A. Calculate h((g ◦ f)(a)) and (h ◦ g)(f(a)). Are they equal?
3. Use your solutions to (1)–(2) to conclude that h ◦ (g ◦ f) = (h ◦ g) ◦ f.
Find a relation R such that 𝑥+𝑦 2 >1 if A = {0,1, 2} and B ={0, 1, 2, 3}. 2. Find a relation R such that y is a power of x if A = {1, 2, 3} and B = {1, 4, 5, 9}
Consider the sequence (wn) defined recursively by
w2 = 3
wn = (wn-1 (1 - 0.02)) - 2(n + 1)/ n2 for n >= 3.
Write a MATLAB program to compute wn for n = 2, 3, 4, . . . , 10 and display the values n
and wn in two columns with appropriate headings. The program should also compute
and display the sum å10∑10\sum 10
∑10 i=2 wi
Let A be a given finite set and P(A) its power set. Let ⊆ be the inclusion relation on the elements of P(A). Draw Hasse diagrams of (P(A), ⊆) for A={a}; A={a,b}; A={a,b,c} and A={a,b.c.d}.
Determine how many bit strings of length 6 can be formed, where the last bit is 0 and two consecutive 0s are not allowed.
Suppose we are given a Boolean function f(x, y, z)=(x+y)(x+y)(x+2). Find its DN form
Let S = [1,2,4,5,10,20, 25, 50, 100). Then show that 5 forms a lattice under divisibility.
Draw the Hasse diagram also.
a) Suppose P (x, y) denotes the equation8, what will the truth values of the Propositions P (2,2), P (0,4).
#340153 on Dec 2023