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) xm + a1 xm -1+ ....am-1 x + am = 0, ai ∈ 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.
Let's go through each statement one by one and check their truthfulness: --- i) The collection of Venn diagrams is a set. This statement is false. The collection of all Venn diagrams is not a set because Venn diagrams are not well-defined objects within a set-theoretic context. Specifically, there is no clear criterion that defines all Venn diagrams in a consistent way, and they involve visual representations that cannot be described purely by a list of elements or objects in a formal mathematical set. --- ii) \((A \setminus B) \cup C = A \setminus (B \cap C)\) for any three sets ______ __________ ______ _________ _____ _____ ________ _________.
______ ___ ___ ______ ____ _____ __________ ______ ___ __________ _________.
________ _________ _________ ____ ______.
__________ _____ __________ __________ _______ ___ ____ ____ _________.
___ __________ ______ _______ ________ ____ _______ _______.
________ ___ _______ __________ __________ ____ _____ _______ ___ _______.
__________ ______ ________ ___ _________ __________.
____ ______ _____ _________ ________ __________.
__________ _____ _______ ______ ___ ___ ___ ______.
_________ __________ ______ ____ _________ ___ _________ __________ _____ ______ _____ __________.
_________ ________ ____ ________ ___ ___ _________ _______ ____ ________.
__________ _______ ________ _________ ___ _______ ______ ________ ___.
___ __________ ______ ___ ____ _____ _______ ________ ________ ___.
__________ _________ __________ ____ _____ ________ ________ _____ ________ __________ __________.
_________ ____ _________ ______ ____ ____ _______ ____ ____ ________ _____ __________.
__________ _________ _____ ____ _______ ________.
___ _____ _______ ___ ________ ___ ________ _______ _________ ___ __________.
_______ _____ __________ ________ _______ ___ ___ ___ _____ _______.
____ _________ ___ __________ _____ _______ _____ _______ ________ ________ _____.
______ ___ ______ _______ ____.
____ __________ _______ ________ _________ ____.
_______ _____ ______ _______ _____.
___ _______ ___ ___ ___ __________.
________ _________ ___ __________ _________ __________ ______ ________ _____ ______.
______ _______ _________ ___ _________ __________ ____.
_____ ____ ______ ________ ____ ___ _____ ___ _________ ____.
________ ___ _______ __________ __________ ____ ________ ___ _____ _____ _________.
_____ __________ ____ ____ ______ _____ ________ __________.
_____ ____ ___ ______ _______.
__________ __________ ________ ____ ________ ________ _________ ____ ___.
_____ _____ _________ __________ ________ __________ ___ _____ _________ _________ ____.
_____ _______ _________ _____ _________.
_______ __________ ________ ____ ______ ____ ______ ______ _________.
_______ _______ _______ _____ _____ ____ _______.
________ _________ __________ _________ _______.
__________ ________ _____ _______ ____ __________ _____ _____ __________.
_________ _________ ____ _____ ____ _____ ______ ____ _______ _________ _____.
_______ __________ __________ _________ __________ ______ ___ ________ ____ ______ ______ _________.
________ ___ _________ _____ ______ ___ ______ _____.
_________ __________ _____ __________ _________ ________ _________ _____ _________ ______.
_______ _____ ____ ___ ___ _________ __________.
___ ______ _______ _________ ________ ______ ______ _____ ___ ______ ______.
___ ____ _______ ___ _________ _________ ______ ____.
______ ___ _____ ____ ___ _____ __________.
_________ ______ _______ ______ ______ ___ ___ ________.
_________ _________ __________ _____ _____.
______ ______ ____ _____ _____.
________ __________ _____ _______ ___.
______ ___ ____ ______ ___ _________.
__________ ___ ___ ___ ____ _______ ______ ___.
_____ _________ ______ ________ __________ ________ _________ ________ ____ _____ __________ ______.
______ __________ _____ _____ ________ ________ ________ ___.
_______ _____ ___ ________ __________ _____ _____.
__________ ____ __________ __________ _________ _____ _____ _____ ____ ___ ____ _____.
____ __________ _______ ___ ______ ______ ______ ___ ___.
_____ __________ _____ _____ ___.
_______ ________ ___ ____ ______ ________ _______ __________ _____ __________.
_______ __________ ____ ________ _______ ________ _____ _______ ________ ___ _______.
______ ________ ______ ________ ___ __________ ______ ____ ___ _____ _________ __________.
_________ ________ _______ ____ _______ ________ ______.
Get Full Answer on WhatsApp
Give examples, with justification, of the following:
i) two non-zero, 3×3 matrices A and B , with A| = 0 |B| = 5/7 i;
ii) two non-singular 2× 2 matrices C and D , with |C| = √2| D |.
Find the roots of the equation 2x³-x2-22x-24=0, if two of them are in the ratio 3:4.
Solve by substitution, the system you have obtained in 5(a).
Show that
Solve x4-8x3+21x220x+5=0 given that the sum of two of its roots is 4.
Draw a Venn diagram of sets B,A and C where
What is the universal set you have chosen? Justify your choice of sets in the diagram.
Solve by substitution, the system you have obtained in 5(a).