Find , and the number of elements in it, where
, and
.
समुच्चय (A={3n+2 \mid 1\le n\le 10}) है। (n=1,2,\dots,10) रखने पर [ A={5,8,11,14,17,20,23,26,29,32}. ] समुच्चय (B={n\in\mathbb Z\mid 1\le n\le ____ _______ ______ _______ ___ ___ _______ __________ ________ __________.
__________ ___ ______ _________ __________ _______ ______ _____ ______ ____.
__________ __________ _______ ____ ___ ___ ___.
________ _________ _____ ____ ______ ____ ___ __________ __________.
_______ ______ _______ __________ ________ _______ _________ _____ _____ _______ ___ ______.
________ ____ ________ ___ __________ ______.
____.
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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 .
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’.
मान लीजिए कि . दर्शाइए कि
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’.
, द्वारा निरूपित रैखिक समीकरणों का एक निकाय, जहां A उपरोक्त (ii) में दिया आव्यूह है।
ख) रैखिक निकाय
उपरोक्त (i) के आव्यूह का परिवर्त;
Find , and the number of elements in it, where