The domain of definition of the function is
(A) [1,4]
(B) [1,0]
(C) [0,5]
(D) [5,0]
Solution: (A)
Given that
For domain of ,
Let be a relation on the set
The relation
is
(A) a function
(B) transitive
(C) not symmetric
(D) reflexive
Solution: (C)
Since, and
So, R is not a function.
Since, and
but
So, R is not transitive
Since, but
so, R is not symmetric
Since, so, R is not reflexive
The domain of the function
(A)
(B)
(B)
(B)
Answer: (B)
Explanation:
We must have
This is only possible when
Let R be a relation defined as if
. Then, the relation
is
(A) Reflexive
(B) Symmetric
(C) Transitive
(D) None of these
Answer: (B) is not reflexive since
is symmetric since if
, then
Thus
R is not transitive. For example,
consider the numbers 3, 7, 3.
since and
, so we have
and
But 3 is not related to 3 as .