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SHOW that every open interval is uncountable
When planning a party you want to know whom to invite. Among the people you would like to invite are three touchy friends. You know that if Jasmine attends, she will become unhappy if Samir is there, Samir will attend only if Kanti will be there, and Kanti will not attend unless Jasmine also does. Which combinations of these three friends can you invite so as not to make someone unhappy?
Are these system specifications consistent? “If the file
system is not locked, then new messages will be queued.
If the file system is not locked, then the system is func-
tioning normally, and conversely. If new messages are not
queued, then they will be sent to the message buffer. If
the file system is not locked, then new messages will be
sent to the message buffer. New messages will not be sent
to the message buffer.”
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)?
