CSE 2500
~(>0, an integer N, such that integer n, if n>N, then n-L )
a
<
>0, such that an integer N.
an integer n, n>N, and n-L
a
Ex 1.
people x, a person y, such that y is xs mom.
(okay)
a person y such that people x, y is xs mom.
(implies y is ever
Assumptions
-A familiarity with the laws of basic algebra is assumed. (Appendix A)-three properties of equality: if A=B then B=A and if A=B and B=C then A=C.
-assume that there is no integer between 0 and 1 and that the set of all integers is closed
under
Assumptions
-A familiarity with the laws of basic algebra is assumed. (Appendix A)-three properties of equality: if A=B then B=A and if A=B and B=C then A=C.
-assume that there is no integer between 0 and 1 and that the set of all integers is closed
under
Assumptions
-A familiarity with the laws of basic algebra is assumed. (Appendix A)-three properties of equality: if A=B then B=A and if A=B and B=C then A=C.
-assume that there is no integer between 0 and 1 and that the set of all integers is closed
under
CSE 2500: HW2 Solutions
Answer 1.
Answer 2.
20(b) Today is New Years Eve and tomorrow is not January.
(c) The decimal expansion of r is terminating and r is not rational.
(e) x is nonnegative and x is not positive and x is not 0.
23 (b): Converse: If tomo
CSE 2500: HW1 Solutions
Answer 1.
(b) T = cfw_0, 2. This is because (1)k is 1 whenever k is either zero or even, and 1 whenever k is
odd. The result is the same even if k is negative since the inverse of 1 remains 1.
(e) W = . There are no elements in W b
Exercise Set 3.1
4, 6, 7, 10, 12, 16, 17, 21, 22, 23, 24, 26, 27, 30, 33.
4. Let Q(n) be the predicate n^2 30.
a. Write Q(2),Q(2),Q(7), and Q(7), and indicate which of these statements are true and which
are false.
Q(2) : 4 30
Q(-2): 4 30
Q(7): 42 30 FAL
Exercise Set 2.2
4. If you fix my ceiling, then I will pay rent.
6.
p
q
~p
(p V q)
F
F
T
T
F
T
F
T
T
T
F
F
F
T
T
T
(~p ^ q)
(p V q) V (~p ^ q)
F
T
T
F
F
T
T
T
10.
p
q
r
(p r )
(q r)
(p r ) (q r)
F
F
F
T
T
T
Question 1. (10 points) Exercises 9, 10, 12, 18 and 20 from exercise set 5.3 (page 266).
Question 2. (10 points) Exercises 26, 27, 28 and 29 from exercise set 5.3 (page 267).
5.3
9) 7^n -1 is divisible by 6 for all integers n greater than or equal to 0
Q
Sharra Neely
CSE 2500
Homework 2
12. a.
P
Q
T
T
F
F
F
T
The statement does not necessitate that if Q is true, P must be true, only that if P is true, Q must be true.
b.
P
Q
~P
~Q
T
T
F
F
F
F
T
T
F
T
T
F
Inverse error also relies on the converse error. Q b
Sharra Neely
CSE 2500
Hw #5
4.5
6. The ceiling would simply be itself as the ceiling function is regards to round of non-integer values.
Since K is an integer, it would remain unchanged.
7. The ceiling of this function would be k+1, as the ceiling functio
Sharra Neely
Homework 4
CSE 2500
3.4:
2. 0 is even
3. a/b + c/d = (2*5+3*4)/(3*5) = 22/15
5. 1/0 is not an irrational number
6. The program is not correct
9. Invalid, inverse error, ~P(x) does not necessarily mean ~Q(x)
10. True, the conclusion is a resul
if, then
pq
p only if q
p q
biconditional - p if and only if q
pq
qp
p q
p is sufficient AND a necessary condition for q
the biconditionl statement variables p,q.
p if and only if q, denoted by pq is true if both p and q have the true value
P
T
T
F
F
Q
Getting started: Writing proofs
Identify starting point and conclusion to be shown
EX: graphs G, if G is complete and bipartite, then G is connected.
Starting point: suppose G is a particular but arbitrarily chosen graph such that G is
complete and bipart
CSE 2500 09-08-15 Notes
Cartesian Products
Given elements a and b, the symbol (a,b) denotes the ordered pair consisting of a and b,
together with the specification that a is the first element of the pair and b is the second element.
ex.
cfw_1,2 = cfw_2,1