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Are these system specifications consistent? “The router
can send packets to the edge system only if it supports the
new address space. For the router to support the new ad-
dress space it is necessary that the latest software release
be installed. The router can send packets to the edge sys-
tem if the latest software release is installed, The router
does not support the new address space.”
Are these system specifications consistent? “The system
is in multiuser state if and only if it is operating normally.
If the system is operating normally, the kernel is func-
tioning. The kernel is not functioning or the system is
in interrupt mode. If the system is not in multiuser state,
then it is in interrupt mode. The system is not in interrupt
mode.”
If 4 cards are selected from a standard 52- card deck must be at least 2 be of the same suit.Why?
Q.1 Prove by contrapositive that if n = a*b, where a and b are positive integers, then
a ≤ √n or b ≤ √n
Prove by contrapositive that if n = a*b, where a and b are positive integers, then
a ≤ √n or b ≤ √n
ind the smallest relation containing the relation {(1, 2), (1, 4), (3
, 3), (4, 1)} that is
a)
reflexive and transitive.
b)
symmetric and transitive.
c)
reflexive, symmetric, and transitive.
In general, a statement involving n variables x1 , x 2 ,…, x n can be denoted by
P( x1 , x 2,…, x n ) and is the value of the predicate P at the n-tuple (x1 , x2 ,…, x n ).
(a) Suppose Q(x , y) denotes the statement “ x=y+3 .” What are the truth values of the propositions Q(1,2) and Q(3,0)?
(b) Let R(x , y , z) denote the statement “ x+y=z .” What are the truth values of R(1,2,3) and R(0,0,1)?
In general, a statement involving n variables x1 , x 2 ,…, x n can be denoted by P( x1 , x 2 ,…, x n ) and is the value of the predicate P at the n-tuple (x1 , x2 ,…, x n ) . (a) Suppose Q(x , y) denotes the statement “ x=y+3 .” What are the truth values of the propositions Q(1,2) and Q(3,0)? (b) Let R(x , y ,
{1,2,3,4,6,9}find maximal and minimal and least and greatest number
5.
Which relation on the set {1, 2, 3, 4} is an equivalence relation and contain {(1, 2), (2, 3), (2, 4), (3, 1)}.
6.
Find the transitive closures of the relation {(1, 1), (1,4), (2,1), (2,3), (3,1), (3, 2), (3,4), (4, 2)} on the set {1, 2, 3, 4}.
7.
Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1, 3), (2, 3), (2, 4), (3, 1), (3, 4), (3, 5), (4, 2), (4, 5), (5, 1), (5, 2), and (5, 4).
Find a) R3 b) R4
8.
Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b speak a common language}
#340153 on Dec 2023