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Let A be the set of all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ and R be a relation on A such that $R = \{(f, g): f(0) = g(1)$ and $f(1) = g(0)\}$. Then R is :

Let A = {1, 2, 3, ...., 100} and R be a relation on A such that R = {(a, b): a = 2b+1}. Let (a1, аг), (аг, аз), (аз, а4),...., (ak, ak+1) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is
equal to :

Let A = {-3, -2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if 0 < x² + 2y < 4. Let l be
the number of elements in R and m be the minimum number of elements required to be added in R to make it a
reflexive relation. Then l + m is equal to

Let A = {-2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by Ry if and only if y = max{x, 1}. Let I be the
number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it
reflexive and symmetric relations, respectively. Then l + m + n is equal to

Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x,y} ∈ {3, 4}. Then among the statements
(S₁): The number of elements in R is 18, and
(S2): The relation R is symmetric but neither reflexive nor transitive

Assertion: The boiling point of water is higher at lower elevations. Reason: Atmospheric pressure increases as elevation decreases.