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
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
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
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
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
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 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