State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Show that the relation R in the Set A = {1, 2, 3, 4,5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the equivalence classes of R.
How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.
Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b)R(c, d) if a + d = b + c. Find the equivalence class [(1,3)].
Let f : X -> Y be a function. Define a relation R on X given be R = {(a, b) : f(a) = f(b)}. Show that R is an equivalence relation ?
Check whether the relation R in the set R of real numbers, defined by R = {(a, b) : 1 + ab > 0}, is reflexive, symmetric or transitive.
Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.
Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.
If and are two unit vectors such that + is also a unit vector, then find the angle between and
If A is a 3 × 3 matrix, whose elements are given by , then write the value of .
State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
If A is a square matrix such that A² = I, then find the simplified value of (A – I)³ + (A + I)³ – 7A.