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Are these system specifications consistent? ”The file system is not locked only if new messages will be queued. If the file system is not locked, then the system is functioning normally, and conversely. For new messages are not queued, it is necessary that they will be sent to the message buffer. Whenever the file system is not locked, new messages will be sent to the message buffer. New messages will not be sent to the message buffer.
An orientation of a graph G = (V, E) is any directed graph G0 = (V, E0 ) arising by replacing each edge {u, v} ∈ E by the directed edge (u, v) or by the directed edge (v, u). Show that for every planar graph there is an orientation such that each vertex has at most five outgoing edges.
If we have two graph G = (V, E) and G0 = (V, E0 ) on the same set V of vertices we call the union G ∪ G0 the graph (V, E ∪ E0 ). Next we have two claim about the chromatic number χ(G ∪ G0 ) of G ∪ G0 .Prove that χ(G∪G0 ) ≤ χ(G)∗χ(G0 ). Hint: consider assigning a color to each vertex in V based on its color in colorings of G and G0 .
He relation (a,b) such that "a" and "b" have the same age ,is defined on the sets of all people.Is it equivalent relation?
Check whether the relation defined by{(a,b)}| a is cousin of b}defined on the sets of all human being is an equivalence or not?
translate the statement "The product of any two positive integers is always positive"into logical expression(using Nested Quantifiers)
Show that among 2000 student in a school, at least six were born on the same day of the leap year
Make a truth table for the given expression.
12. (~p∧q) ∨ (p∧~q)
13. (p∧~q) ∨ r
14. ~[(p∧~q) ∨ ~p]
15. (p∨q) ∧ ~(~q∧r)
16. (~p∧q) ∨ (~p∨q) 17. ~[(p∨q) ∧ ~q]
The Mathclub, VIT-AP wants to conduct a group event for its members. So the club president has to fix the group size the event. When he tries to fix the size to be 5 members in each group, 4 members are left; when he tries to fix the size to be 6 members in each group, 5 members are left; When he fixes the size to be 7 members in each group, 6 members are left. What is the smallest number of members that the club has?
Show that ~ (p → q) and p ∧~q are logically equivalent. (Hint: you can use a truth table to prove it or you apply De Morgan law to show the ~(p → q) is p ∧~q.
