Sets-II Starter Quiz-2

Suppose that R is transitive relation on the set Z of all integers, and for any two integers a, b ∈ Z, if |a – b| = 2 then a R b.

Which of the following is true ?

The size of a proper subgroup of a finite group G is 31. The size of the smallest possible group G is ____.

Let X be an empty set. How many number of elements in P(P(P(X))) where P(X) is power set of X?

The number of relations which are either symmetric or antisymmetric with 4 elements are ________.

A binary operation Η on a set of integers is defined as . Which one of the following statements is true about Η?

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?