Answer to Question #44523 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) For any two sub sets A and B of a set U, AB=BA.
ii) The contrapositive of ‘If Lalita is good at mathematics, then her daughter passes the maths exam’ is the statement ‘If Lalita is not good at mathematics, then her daughter fails the maths exam’.
iii) The geometric representations of z and z1 (for z

0, z

C) are the reflections of each other in the x-axis.
iv) Arg
.44
v) Any polynomial over Q can have at most one root in C \ R.
vi) If a

R, then det ([a])
.0
vii) If
101,,
are positive real numbers with arithmetic mean A, then their harmonic mean is A1.
viii) Any two linear equations in the variables x and y will have infinitely many common solutions.
ix) {Descartes, DeMorgan, }is a set.
x) A matrix representation of x+yz=3 is [x y z]
111
= [3].