On set A = {1, 2, 3}, relations R and S are given by
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},
S = {(1, 19, (2, 2), (3, 3), (1, 3), (3, 1)}.
Then,
R S is an equivalence relation
R S is reflexive and transitive but not symmetric
R S is reflexive and symmetric but not transitive
R S is symmetric and transitive but not reflexive
If the function f : , then f is
one-one but not onto
onto but not one-one
neither one-one nor onto
both one-one and onto
Let f: then
f is one - to - one
f is onto
f is one - to - one but not onto
f is onto but not one - to - one
If A and B are two matrices such that AB = B and BA = A, then A2 + B2 equals
2AB
2BA
A + B
AB
C.
A + B
Given, AB = B and BA = A
Now, A2 + B2 = A . A + B . B
= A(BA) +B(AB)
= (AB)A + (BA)B
= BA + AB = A + B
A relation p on the set of real number R is defined as {xy: xy > 0}. Then, which of the following is/are true?
is reflexive and symmetric
is symmetric but not reflexive
is symmetric and transitive
is an equivalence relation
The function f(x) = x2 + bx + c, where b and c real constants, describes
one - to - one mapping
onto mapping
not one-to-one but onto mapping
neither one-to-one nor onto mapping
For any two real numbers we define , if and only if = 1. The relation R is
reflexive but not transitive
symmetric but not reflexive
both reflexive and symmetric but not transitive
an equivalence relation
We define a binary relation on the set of all 3 x 3 real matrices as A B,if and only if there exist invertible matrices P and Q such that B = PAQ-1 .The binary relation is
neither reflexive nor symmetric
reflexive and symmetric but not transitive
symmetric and transitive but not reflexive
an equivalence relation
In the set of all 3 x 3 real matrices a relation is defined as follows. A matrix A is related to a matrix B, if and only if there is a non-singular 3 x 3 matrix P, such that B = P-1AP. This relation is
reflexive, symmetric but not transitive
reflexive, transitive but not symmetric
symmetric, transitive but not reflexive
an equivalence relation
For any two real numbers a and b, we define a R b if and only if sin2(a) + cos2(b) = 1. The relation R is
reflexive but not symmetric
symmetric but not transitive
transitive but not reflexive
an equivalence relation