Assignment1
0. [1pt] What file format should assignments be submitted in? What are the consequences if it is not submitted in that format?
Please use the knowledge about set theory to solve the following problems.
1. [1 pts] |{Ø}| = ___ .
A. If ℕ is the set of Natural Numbers, then the size of ℕ is ∞.
B. A power set is a set of sets.
C. For a finite set, the size of its power set is greater than its size.
D. If S – P = Ø, then S = P (Both S and P are sets).
E. The elements of a set can be the set
3. [2 pts] Let A = {0, 2, 4}, B = {1, 3, 5}, C = {3, 4, 5}. Find
a) A ∪ (B − C)
b) A × (B − C)
c) |{𝑃(𝐴) − 𝑃(𝐶)}|
d) P(A) ∩ P(B − C)
4. [2 pts] We use RLT5 to note the “Less Than” Relation on natural numbers smaller than 5.
(1) Please define RLT5 as the set of ordered pairs mathematically. Example: Addition Relation on natural numbers smaller than 2 is
AddR2: N2→N2 =df {(0,0), (0,1), (1,0), (1,1)}
(2) RLT5 is .
a. Universal b. Identity c. Reflexive d. Irreflexive
e. Symmetric f. Antisymmetric g. Connected h. Transitive
5. [2pt] Let P = {0, 1, 2}. R = {(0,0), (0,1), (1,0), (1,1), (2,2)} is a relation on P.
a) (True or False) R is an equivalence relation.
(b) If (a) is true, find the equivalence class [0]≡ and the quotient set of P defined by R. If (a) is not true, find a counterexample.
