Questions
1
Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
Answer:transitive but not symmetric
2
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
Answer:reflexive but not symmetric
is the domain of
7
If f : R → R such that f(x) = 3x then what type of a function is f?
Answer:one-one into
8
The maximum number of equivalence relations on the set A = {1, 2, 3} are
Answer:5
9
Let f: N → R be the function defined by f(x) = 2x−1/2 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 3/2 is
Answer:None of these
10
If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
Answer:1/3 (x + 4)
11
If f(x) is an odd differentiable function on R, then df(x)/dx is
Answer:an even function
12
Let A = {1,2,3} . Which of the following relations is a function from A to A ?
Answer:{(1,1),(2,1),(3,2)}
13
Let A = {a,b,c} and R = {(a,a),(b,b),(c,c),(b,c),(a,b)} be a relation on A, then R is
Answer:reflexive
14
Let ƒ : N → N be defined by the rule f (x) = 2x + 1 for all x ∈ N, then f is
Answer:one - one
15
Let A = {1,2,3} and B = {2,3,4}, then which of the following is a funtion from A to B ?
Answer:{(1,3),(2,3),(3,3)}
16
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
Answer:2
17
let A = {1,2,3} . Which of the following functions on A is invertible ?
Answer:f = {(1,2),(2,3),(3,1)}
Chapters
