यदि A और B क्रमशः समपूर्णांकों और विषम पूर्णांकों के समुच्चय हैं, तो  और  ज्ञात कीजिए।

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’.

अपने इग्नू अध्ययन के संदर्भ में निम्नलिखित दीजिए :

i) निहितार्थ का एक उदाहरण;

ii) उपरोक्त (i) में दिए गए अपने कथन का विलोम;

iii) उपरोक्त (i) में दिए गए अपने कथन का प्रतिधनात्मक;

iv)  का प्रयोग करते हुए एक कथन;

v)  का प्रयोग करते हुए एक कथन;

क) दर्शाइए कि .
ख) मान लीजिए कि . दर्शाइए कि .

 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 .

उपरोक्त (i) के आव्यूह का परिवर्त;