Explanation
R is Reflexive and transitive.Here 6 is a multiple of 2 but 2 is not a multiple of 6.∴ R is not symmetric
n is a factor of m but not necessary m is a factor of n so R is not symmetric
If x = 8 – 2y then R = {(2, 3), (4, 2), (6, 1)}
since domain of f and domain of composite function gof are same (–1, 1)
A = {3, 6, 9, ….}, B = {5, 10, 15,….}
A ∩ B = {15, 30, 45, ….}
(A ∪ B) = {a, b, c, d, l, f, m}
C ∩ (A ∪ B) = (a, l, m, o) ∩ {a, b, c, d, l, f, m}
= {a, l, m}
The set A is the set of all points on the curve y = ex and the set B is the set of all points on the line y = x passing thro’ the origin and making an angle 45° with the - axis. These two curves do not intersect.
∴ A ∩ B = Ø
n (A) = 10
∴ total no. of distinct functions from A to A = 1010
Since n (A) = n ∴ P(Α) has 2n elements.
Since a binary operation on S is a function from S × S to S ∴ total number of binary operations on S is the total number of functions from S×S to S which is nn2
The total number of mapping from A to B is 2nof which the 2 mappings for all and f(x) = a for all 1 ≤ x ≤ n and g(x) = b for all 1 ≤ x ≤ n are not surjective.
∴ the no. of surjective mappings = 2n – 2
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