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) Eliminating z from ,
and
gives
.
ii) The roots of are given by
.
iii) .
iv) Given any n positive numbers in , the product of their harmonic mean and their arithmetic mean is 1.
v) If A and B are two sets such that is empty, then either
or
.
vi) For any .
vii) The geometrical representation of the set is a point.
viii) Any finite set is a subset of .
ix) Every biquadratic equation has at least one real root.
x) The converse of the statement, ‘Every student of MTE-04 has completed FST-01’, is ‘Every student of FST-01 has completed MTE-04’.
i) False. Eliminating a variable from multiple equations does not always produce the same resulting equation; it depends on the specific equations. Counterexample: Equations: (x + y + z = 3) and (x - y + z = 1). Eliminating (z) gives (2y = 2 \implies y = 1), not a single equation in the form “equation”. ii) True. The roots of a quadratic equation (ax^2 + bx + c _____ _____ ___ _________ ___ ______ ____ _______.
____ __________ __________ _______ ______ ___ ______ _____ __________ __________ ____ _____.
__________ ______ _______ _____ ______ ___ _____ ________ _________.
_____ ______ ____ _____ _______.
_______ _________ _______ _________ _______ _________ _________ _____ ___ _________ ____.
_______ _________ _______ _________ ____ ________ _______ ____.
___ ________ ________ ____ _______ ________ _____.
__________ ______ _____ ____ __________ __________ ___ _________ _________ _____ ____.
______ __________ _________ ___ _______.
___ _________ __________ ________ _____ ______ _______ _________ ___ _____ _______.
___ _____ _______ _________ __________ ______ ______ ___ _______ ______ _______.
___ ______ ______ ________ _____ ___.
________ ___ __________ ________ ___ __________.
______ __________ ____ _______ ________ _____ _____ ____ ________.
_______ ___ ______ _________ ________ _______.
_________ _________ _________ ______ ___ ________ _________ _____ ___ ____.
____ ___ ____ ___ ______ ______ ______ ________ ___ ______ ______.
___ _____ ____ __________ __________ _______ __________ _____ ________ _________.
______ ____ ____ ________ ___ _______ ______.
__________ _____ ___ ___ ________ _______ _____ _____ _____ ___ ______ _____.
____ ____ _______ _______ ___ _________ __________ _________ _________ _________ _______.
________ _____ ________ ___ __________ _______ ______ _________ ____ _______ ______.
___ ______ ______ _________ ___ _____ ____ ________ ______ _________.
_____ ______ ___ _____ ___ __________ _______ __________ ________ _________ ________ ________.
__________ ____ __________ ________ __________ _________ ________ _______.
__________ ___ ______ ________ _____ ______ ________ ________ ____.
________ ______ _____ ________ _________.
_____ ________ ___ _________ ____ __________.
________ ________ ____ _________ _____ ____ ____ __________ _______ _______ _______.
__________ ___ __________ __________ ______ ____ ___ ______ ___ __________.
____ ____ ___ ____ __________ ___ _______ _____ ___ _______ ____ ______.
__________ _____ ______ _____.
Get Full Answer on WhatsApp
वह त्रिघात समीकरण ज्ञात कीजिए जिसके मूल के मूलों के घन हैं।
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) Eliminating z from ,
and
gives
.
ii) The roots of are given by
.
iii) .
iv) Given any n positive numbers in , the product of their harmonic mean and their arithmetic mean is 1.
v) If A and B are two sets such that is empty, then either
or
.
vi) For any .
vii) The geometrical representation of the set is a point.
viii) Any finite set is a subset of .
ix) Every biquadratic equation has at least one real root.
x) The converse of the statement, ‘Every student of MTE-04 has completed FST-01’, is ‘Every student of FST-01 has completed MTE-04’.
Using the method of substitution, obtain the solution set in , of the following:
i)
ii)
iii)
In the context of your IGNOU studies, give the following:
i) an example of an implication;
ii) the converse of your statement in (i) above;
iii) the contrapositive of your statement in (i) above;
iv) a statement using ;
v) a statement using .
, तथा इसमें अवयवों की संख्या, ज्ञात कीजिए, जहां
, तथा
.
ii) दो समुच्चय C और D, दिए रहने पर, उन पर किन प्रतिबंधों के अधीन और
में अवयवों की संख्या समान होगी? अपने उत्तर के कारण दीजिए।
वास्तविक जीवन की स्थिति की एक ऐसी समस्या दीजिए, जिसका गणितीय सूत्रीकरण है
) Find the values of for which ai is a solution of
. Also find all the roots of this equation.
b) Find all the roots of 3i - 3. Also show any one of them in an Argand diagram.