Search & Filtering
- ∅ ⊆ A (true or false) 2.n(∅) = 0 (true or false)
1. Represent the following sets in tabular or listing form:
(i) A={x:x^2 - 3x + 2 = 0}
(ii) B= { x:x is an integer and 1 < x < 7}
Consider the following two arguments:
A. If Fred wanted me fired then he would go to the boss. Fred is going to the boss. Therefore Fred wants to get me fired.
B. Max is a cat or Max is a mammal. Max is a cat. Therefore Max is not a mammal.
Which of the following is true?
Find (showing your reasoning) a formula for the term tn of the sequence defined by t1 = 4; tn = 2tn−1, n ≥ 2.
[{1,2,3,4,5}, <=], Draw its Hasse Diagram.
Q1. Let {1,2,3,4,6,9} with the partial order of divisibility. Draw its Hasse Diagram
Q2. [{1,2,3,4,5}, s], Draw its Hasse Diagram
Determine an, the number of words of length n on the alphabet {a, b, c} which
do not contain the substring ab. For instance, a3 = 21 since there are 21 such words
with 3 letters, namely:
aaa aac aca acb acc baa bac
bba bbb bbc bca bcb bcc caa
cac cba cbb cbc cca ccb ccc.
Let α, β be roots of the equation x^2− 3x − 1 = 0. For each nonnegative integer n,
let y_n = α^n + β^n
. Show that gcd(y_n, y_(n+1)) = 1 for each nonnegative integer n.
Use the Well Ordering Principle to prove that any integer greater than or equal to 23 can be represented as the sum of nonnegative integer multiples of 6, 7 and 17.
Encrypt the message ATTACK using the RSA cryptosystem with n = 43 · 59 and
e = 13, translating each letter into integers and grouping together pairs of integers, as
done in example 11 in the textbook and in the classnotes.
