Sets, Relations and Functions
Sets and their representation; union, intersection and complement of sets and their algebraic properties; power set; relation, types of relations, equivalence relations; functions — one-to-one, into and onto; composition of functions.
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Take a full mock →Q1 · Sets, Relations and Functions · EASY
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then the number of elements in (A ∪ B) × (A ∩ B) is:
Q2 · Sets, Relations and Functions · HARD
Let R be a relation on the set N of natural numbers defined by R = {(x, y) : x, y ∈ N and x² - 4xy + 3y² = 0}. Then R is:
Q3 · Sets, Relations and Functions · EASY
If f : R → R is defined by f(x) = 3x - 5 and g : R → R is defined by g(x) = x² + 3, then (g ∘ f)(2) equals:
Q4 · Sets, Relations and Functions · MEDIUM
Let A = {1, 2, 3, 4, 5} and let R be a relation on A defined by R = {(x, y) : |x - y| is divisible by 2}. Then the number of elements in R is:
Q5 · Sets, Relations and Functions · MEDIUM
Let f : R → R be defined by f(x) = (x + 1)/(x - 1) for x ≠ 1. Then f(f(x)) equals: