Related InterviewSolutions

• Find the domain of function `f(x)=3/(sqrt(4-x^(2)))log(x^(3)-x)`
• Define a relation on a set. What do you mean by the domain and range of a relation? Give an example.
• Let `A={2,3,4,5,6,7,8,9}` Let `R` be the relation on A defined by `{(x,y):x epsilonA,yepsilonA` & `x^(2)=y` or `x=y^(2)`}. Find domain and range of `R`.
• Let R = {(a, b) : a, b ∈ N and b = a + 5, a < 4}. Find the domain and range of R.
• Let R \(=\begin{Bmatrix}(a,\frac{1}{a}):a \in N &and &1<a<5\end{Bmatrix}\)Find the domain and range of R.
• Let R = {(a, b) : b = |a – 1|, a ∈ Z and la| < 3}. Find the domain and range of R.
• Let R = {(a, a3) : a is a prime number less than 5}. Find the range of R.
• Find the domain and range of the relation R = {(-1, 1), (1, 1), (-2, 4), (2, 4)}.
• Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R2 = {(2, 2), (3, 1), (1, 3)}, R3 = {(1, 3), (3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is(i) reflexive(ii) symmetric(iii) transitive.
• Three relations R1, R2 and R3 are defined on a set A = {a, b, c} as follows: R1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c, c)}R2 = {(a, a)}R3 = {(b, c)}R4 = {(a, b), (b, c), (c, a)}.Find whether or not each of the relations R1, R2, R3, R4 on A is(i) reflexive (ii) symmetric and (iii) transitive.