Qn:(a)
given A and B are disjoint sets
shade in venn diagram
(i)B∩C (ii)A−(B∪C) (iii)(B∪C)−A
Qn:(b)
Given that ∣A∣=19 ∣B∣=23 ∣C∣=24
∣A∪B∣=30 ∣(A∩B)−C∣=5 ∣(B∩C)∣=10
∣(A∪B)^′ ∣=20 and ∣C−(A∪B)∣=10
then find
(i)∣(A∩C)∣ (ii)∣(B−′C)∣′
(iii)∣𝛍∣ (iv)∣(B′∪C)∩A′∣
Let function f(x) be defined as
f(x)= x^2 +bx+c , where b,c∈R .
And f(1) − 2f(5) +f(9) =32.
Find no. of ordered pairs (b,c)
such that ∣f(x)∣≤8 ∀ x∈ [1,9] ?
1) prove that ∀(a,b)∈R^2 ∣sinb −sina∣≤∣b−a∣
2)let give the sequence x_0 =0 and
x_(n+1) =a +(1/2)sin(x_n ) prove that for m≥n
∣x_m −x_n ∣ ≤ ((∣a∣)/2^(n−1) )
3) prove that (x_n ) is convergent and its limit is solution
of the equation x = a +(1/2) sinx .