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GATE 2020 : Discrete Maths Quiz 5

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Question 1

Let X and Y be finite sets and f: X Y → be a function. Which one of the following statements is TRUE?

Question 2

Consider the set of all functions f : {0,1,…..,2014} → {0,1,…..,2014} such that f(f(i)) = I, for 0 ≤ i ≤ 2014. Consider the following statements.

P. For each such function it must be the case that for every i, f(i) = i,

Q. For each such function it must be the case that for some i, f(i) = i,

R. Each such function must be onto.

Which one of the following is CORRECT ?

Question 3

Consider the poset (Z, +) where Z represents set of all integers {0, +1, -1, +2, -2, +3, -3, ….} and the binary operation is addition. Choose the most appropriate option regarding the given poset among the following.

Question 4

Consider the following statements :
S1 : The number of relations that are both reflexive and asymmetric is 0.
S2 : The number of relations that are both symmetric and asymmetric is 0.
Which option is correct?

Question 5

What is the number of different n x n square symmetric matrix of order n, having each element either 0 or 1?