GATE 2020 : Discrete Maths Quiz 4 (App update required to attempt this test)

To be a Boolean Algebra, the lattice must have the following properties:

Let A = {0, ±1, ±2, 3}, Consider the function f : A → R where R is the set of all real numbers, defined by
f(x) = - 2 + 3x + 1
for x ∈ A. The range of f is?

Consider the following statement?

(1) If R and S are equivalence relations then R ∩is also an equivalence relation.

(2) If R and S are equivalence relations then R U S is also an equivalence relation.

(3) If a set contains 3 elements then the number of an equivalence relation is 5.

(4) If the set contains 4 elements then the number of equivalence relations is 15.

Identify the false statement.

Let S = {5, 10, 25, 27, 35} be ordered by divisibility. Then the maximal and minimal element of S.

A group (G, *) is called a cyclic group if there exists an element a ∈ G, such that every element of ‘G’ can be written aⁿ for some integer n. Then ‘a’ is called generating element / generator. Consider the following group G = ( {1, 2, 3, 4, 5, 6}, ⊗₇), where ⊗₇ is multiplication modulo 7 operation. Let X be the number of generator of G. And Y be the sum of these generator. Find X + Y is _________________?