How many equivalence relations on the set {1, 2, 3} containing (1, 2) and (2, 1) are there in all ?Justify your answer.
Equivalence relations could be the following :
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} and{(1, 1), (2 2), (3, 3), (1,2), (1 ,3), (2 ,1), (2, 3), (3,1), (3,2)}
So, only two equivalence relations.
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} and{(1, 1), (2 2), (3, 3), (1,2), (1 ,3), (2 ,1), (2, 3), (3,1), (3,2)}
So, only two equivalence relations.
State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].
Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.
State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.
If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)
If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.
If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then find P(A/B).
Verify that ax² + by² = 1 is a solution of differential equation
Three cards are drawn without replacement from a pack of 52 cards. Find the probability that
(i) the cards drawn are king, queen and jack respectively.
(ii) the cards drawn are king, queen and jack.