Which of the following statements are true? Justify your answers. (Thi

Question

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.

ii) (A\B) UC=A\(B∩C) for any three sets A, B and C.

iii) If ze R, then |z|=z.

iv) x^m + a₁x^{m -1}+ ....a_m-1x + a_m = 0, a_i ∈ R∀ i = 1, ..., m, has a root in R only if m is an odd number.

v) x > 0 is necessary for x+3>1.

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 > 4, the AM of the first n natural numbers is greater than n +1.

17 Feb 2025

Answer :

Word Count : 606

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