GATE CS 2022 : Discrete Mathematics Revision Quiz - 8

If P, Q, R are subsets of the universal set U, then (P ∩ Q ∩ R) ∪ (P^c∩ Q ∩ R) ∪ Q^c∪ R^c is

Consider the following statements.
P₁:
P₂:

P₃:

` Which of the predicate logic statements represents the following statement.
“there are exactly two apples”.

How many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same suit are chosen ______________?

Consider S = {1, 2, . . . n}, each subset of S represents one vertex in a graph G. Let X and Y be being two subsets of S. There will be an edge between X and Y, if their symmetric difference is equal to 3. For n = 6, the degree of the vertex corresponding to a 3-element subset is __________________?

Note: Symmetric difference of two set is defined A and B is defined as (A\B) U (B\A)

The number of way of distributing 10 identical balls in 3 distinct boxes such that no box is empty is?

In an examination of 9 papers a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is _________.

Consider a set S = {1000, 1001, 1002, ........ 9999}. The numbers in set ‘S’ have atleast one digit as 2 and atleast one digit as 5 are ________.

Which of the following statement is incorrect?

Which of the following complete bipartite graphs will have Hamiltonian cycle?

Consider the below graphs G:

The chromatic number of above graph is

Let the following predicates be given. The domain is all computer science classes.

I(x) = “x is interesting.”

U(x) = “x is useful.”

H(xy) = “x is harder than y.”

M(xy) = “x has more students than y.”

Let P1 :

The correct translation of the above predicate logic statement P1 is:

Let G be a cyclic group of order 128, and ‘a’ be a generator of G. Then the value of Ο(a⁴) will be ________.