GATE PYQ

Discrete Mathematics

Q271.
The symmetric difference of sets A={1,2,3,4,5,6,7,8} and B={1,3,5,6,7,8,9} is:

Q272.
Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?

Q273.
The number of onto functions (surjective functions) from set x={1,2,3,4} to set Y={a,b,c} is __________.

Q274.
What is the possible number of reflexive relations on a set of 5 elements?

Q275.

Q276.
A partial order P is defined on the set of natural numbers as follows. Here \frac{x}{y} denotes integer division. i.(0, 0) \in P. ii.(a, b) \in P if and only if (a \% 10) \leq (b \% 10) and (\frac{a}{10},\frac{b}{10})\in P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153) Which of these ordered pairs of natural numbers are contained in P?

Q277.
The set of all Equivalence Classes of a set A of Cardinality C

Q278.
If P, Q, R are subsets of the universal set U, then (P\cap Q\cap R)\cup (P^{C} \cap Q \cap R)\cup Q^{C} \cup R^{C} is

Q279.
Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are:

Q280.
A binary operation \oplus on a set of integers is defined as x \oplus y= x^{2}+y^{2}. Which one of the following statements is TRUE about \oplus ?