Discrete Math Problems

V is used for logical or

Lemma 8 find four relations from {a,b} to {x,y} that are not functions from {a,b} to {x,y}
a function has a one to one input to output relationship these pairs are functions
A , X
B , X
A , Y
A, X

the remaining pairs are :
X , X
Y , Y
Y , X
X , Y
these are not functions as defined above

changing weather functions go from X to Y or Y to X does not alter the definition

Define functions H and K from the set of real by the following formula: For all x that is a member of the set of reals
Lemma 20 H(x)=(x-2)² and K(x)=(x-1)(x-3)+1

Does H = K
at point x=0
(4,4)
H=(0-2)^2 K= (0-1)(0-3)+1 = 4
point x= 2
(0,0)

equal

exercise 2.1
10. Let p be the statement “DATAENDFLAG is off, q the statement “ERROR equals 0” r the statement SUM is less than 1000”. Express the following sentences in symbolic notation.

10a
DATAENDFLAG is off, ERROR equals 0, SUM is less than 1,000
P^Q^R
Q^R go together per grammar of question

10b DATAENDFLAG is off but ERROR is not equal to 0

but equals not
P ^ ~Q
10c DATAENDFLAG is off , however ERROR is not 0 or SUM is greater than or equal to 1000.
p ^ ( ~Q V R )

10e Either DATAENDFLAG is on or it is the case that both error equals zero and SUM is less than 1,000

Exercise Set 2.3

deduce the conclusion from the premises Assume all are statement variables

p → q
r V s
~s → ~t
~q v ~s
~s
~p ^ r → u
w V t
therefore u ^ w

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