Answer to Question #44524 in Math for JASHVINDER

Question

Which of the following statements are true? Give reasons for 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) {MTE-04, –3, Indira Gandhi} is a set.
ii) For any two sets A and B, A ∪ Bc = A ∩ B.
iii) There is a unique z ∈ C for which z z 1 − = .
iv) The least degree of the polynomial with real coefficients and with roots 2+i, 2i – 1 is 2.
v) If a statement has a direct proof, then it cannot be proved by contradiction.
vi) The equation x = 3 has the same geometric representation regardless of whether it is an
equation in one variable or two variables.
vii) Any system of n linear equations in n – 1 variables has a solution.
viii) The CS inequality is a generalization of the triangle inequality.