Show that 1 + 1/sqrt(2)+ 1/sqrt(n) ≥ sqrt(2(n − 1)) , for n ∈ N, n > 1 .
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Show that 1 + 1/sqrt(2)+ 1/sqrt(n) ≥ sqrt(2(n − 1)) , for n ∈ N, n > 1 .
Write an odd natural number as a sum of two integers m1 and m2 in a way that m1m 2 is maximum.
For any two sets A and B , in a universal set U , prove that
A ⊆ B ⇔ A ∪ B = B .
Prove that 
Find the sum of the 5th roots of unity.
Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that ‘{1, padma, blue} is a set’ is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
iii) If z ∈ R , then | z | = z .
vi) Any system of three linear equations in two variables has no solution.
vii) If a matrix has n2 entries, where n ∈ N , then it is a square matrix.
viii) For n > 2 , the AM of the first n natural numbers is greater than n + 1.