RELATIONS AND FUNCTION
- Let M be the set of men and R is
a relation ‘is son of’ defined on M.
Then, R is
(a) an equivalence (b) a
symmetric relation only (c) a
transitive relation only (d) none
of the above - The relation R = {(1, 1), (2, 2), (3,
3), (1, 2), (2, 3), (1, 3)} on a set A =
{1, 2, 3} is (a) reflexive, transitive
but not symmetric (b) reflexive,
symmetric but not transitive (c)
symmetric, transitive but not
reflexive (d) reflexive but neither
symmetric nor transitive - The order of a set A is 3 and that
of set B is 2. What is the number of
relations from A to B?
(a) 4 (b) 6 (c) 32 (d) 64 - Let X be the set of all graduates
in India. Elements x and y in X are
said to be related, if they are
graduates of the same university.
Which one of the following
statements is correct?
(a) Relation is symmetric and
transitive only (b) Relation is
reflexive and transitive only (c)
Relation is reflexive and
symmetric only
(d) Relation is reflexive symmetric
and transitive - The function f(x)= from R to
R is
(a) one-one as well as onto (b)
onto but not one-one (c) neither
one-one nor onto (d) one-one but
not onto- Let A= {-1, 2, 5, 8}, B= {0, 1, 3, 6,
7} and R be the relation ‘is one less
than’ from A to B, then how many
elements will R contain?
(a) 2 (b) 3 (c) 5 (d) 9 - A mapping f : R R which is
defined as f(x)= cos x ; x R is
(a) one-one only (b) onto only (c)
one-one onto (d) neither one-one
nor onto - Which one of the following
functions f : R R is injective?
(a) f(x)= | | (b) f(x)= ,(c) f(x)= 11, (d) f(x)= -x,- If A= {a, b, c} and R= {(a, a), (a,
b), (b, c), (b, b), (c, c), (c, a)} is a
binary relation on A, then which
one of the following is correct?
(a) R is reflexive and symmetric,
but not transitive (b) R is
reflexive and transitive, but not
symmetric (c) R is reflexive, but
neither symmetric nor transitive
(d) R is reflexive, symmetric and
transitive
10. Let g : R R be a function
such that, g(x)= 2x + 5. Then, what
is (x) equal to?
(a)^ (b) 2x – 5 (c) x - (d)^