Q. 1. Let A = {1,2,3,4} find the number of relations on A containing (1, 2) and (3, 2) which is reflexive transitive but not symmetric giving sufficient reasons.
Q. 2. Let R be the set of real numbers on ‘R’ defined by R = {(a,b) / | a-b | < 5} is not transitive . Prove the above statement by giving two examples.
[ANS (3,6) (6,9) (3,9)
(2,4) (4,8) (2,8) ]
Q. 7. Let f: N --> Y be a function defined by f(x) = x2 + 1 Show that f is one – one and replace Y by a set so that f is invertible. Also find its inverse function.
Q. 8. Let f : R -> R g: R -> R defined by
a. f(x)=x2 + 8 g(x)=3x3 + 1
b. f(x)=x2 + 2x – 3 g(x) = 3x – 4 Show that fog and gof exists and hence find them.
Q. 2. The minimum number of elements that must be added to the relation R = { (1,2), (2,3) } on the set of natural numbers so that it is an equivalence is
a. 4
b. 7 IS THIS THE ANS?
c. 6
d. 5
Q. 3. Let ‘R’ be a reflexive relation on a finite set ‘A’ having ‘n’ elements and let there be ‘m’ ordered pairs in ‘R’. Then
a.
b.
c.
d. none of these.
Q. 4. Let ‘X’ be a family of sets and ‘R’ be a relation defined by ‘A is disjoint from B’ .Then R is
a. Reflexive
b. Symmetric
c. Anti symmetric
d. Transitive
Q. 5. The number of surjections from A = {1, 2, 3, ….. n} on to B = {a, b} is
a. nP2
b. 2n - 2
c. 2n - 1
d. none
Q. 9. Let f(x) = [x] and g(x) = x - [x] then which of the following function is the zero function
a. (f+g) (x)
b. (fg) (x)
c. (f-g) (x)
d. fog (x)