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Saloni Thakur 6 years ago
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Robinpreet Kaur 6 years, 4 months ago
Kung Fu ?? 6 years, 4 months ago
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Divya Thampi 6 years, 4 months ago
Kung Fu ?? 6 years, 4 months ago
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Yogita Ingle 6 years, 4 months ago
The pacemaker is implanted just near the collarbone. If only one lead is needed, it is placed inside the lower-right chamber (the right ventricle). If two leads are needed, the other is placed in the upper-right chamber (the right atrium).
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Gaurav Seth 6 years, 4 months ago
It is correct that politics is more than what politicians do. Politicians as a part of government are involved in politics but politics is not limited to their activities. Politics involves number of various negotiations that go on in society through which collective decisions are made.
- Politics involves the actions of government and its relation to the aspirations of the people.
- Politics involves the struggle of people and its influence on decision making.
- People are engaged in political activity whenever they negotiate with each other and participate in collective activities that are designed to promote social development and resolve common problems.
- For example, residents of localities form associations to solve their common problems and raise these issues at higher level.
- Students form unions in colleges and universities to debate and resolve issues that affect the majority of them.
- Thus, politics is involved in the sphere of life that is related to power, collective decision-making and solving common problems.
Posted by Nistha Yadav 6 years, 4 months ago
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Avinash Saigal 6 years, 3 months ago
Gaurav Seth 6 years, 4 months ago
Psychology is defined as a science which studies mental processes, experiences and. behaviour in different contexts. In doing so, it uses methods of biological and social sciences to obtain data systematically. It makes sense of the data so that it can be organized as knowledge.
Posted by Vansh Trivedi 6 years, 4 months ago
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Gaurav Seth 6 years, 4 months ago
If A & B are two non- empty subsets and we have to prove AxB=BxA iff A=B
Proof:
We will prove this in two parts. In first part we will prove that if A=B then AxB=BxA and in the second part we will prove that if AxB=BxA then A=B.
i) For the first part let us assume that A=B
Then in AxB we can first replace first ‘A’ with ‘B’ (As by assumption A=B) so that it becomes BxB. Now we have AxB=BxB. In the next step we replace ‘B’ with ‘A’ so that BxB can be written as BxA.
Thus we have AxB=BxB=BxA
ii)For the second part we assume that AxB=BxA and then we will prove that A=B. We will prove this by double containment. We will prove that A is subset of B and then B is subset of A .
Let x∈ A and y∈B
Now (x, y) ∈ AxB
But by our assumption AxB and BxA are equal
So (x,y) ∈ BxA implying that x ∈B , sine x is an arbitrarily chosen element, so A is subset of B.
Now let x∈B and y∈A
So (x,y) ∈ BxA
But again since BxA=AxB; therefore x∈A. Thus implying as before that Bis subset of A
Thus from double containment viz. A being subset of B and B being subset of A; we get A=B.
Thus (i) and (ii) complete the proof.
If A & B are two non- empty subsets and we have to prove AxB=BxA iff A=B
Proof:
We will prove this in two parts. In first part we will prove that if A=B then AxB=BxA and in the second part we will prove that if AxB=BxA then A=B.
i) For the first part let us assume that A=B
Then in AxB we can first replace first ‘A’ with ‘B’ (As by assumption A=B) so that it becomes BxB. Now we have AxB=BxB. In the next step we replace ‘B’ with ‘A’ so that BxB can be written as BxA.
Thus we have AxB=BxB=BxA
ii)For the second part we assume that AxB=BxA and then we will prove that A=B. We will prove this by double containment. We will prove that A is subset of B and then B is subset of A .
Let x∈ A and y∈B
Now (x, y) ∈ AxB
But by our assumption AxB and BxA are equal
So (x,y) ∈ BxA implying that x ∈B , sine x is an arbitrarily chosen element, so A is subset of B.
Now let x∈B and y∈A
So (x,y) ∈ BxA
But again since BxA=AxB; therefore x∈A. Thus implying as before that Bis subset of A
Thus from double containment viz. A being subset of B and B being subset of A; we get A=B.
Thus (i) and (ii) complete the proof.
Posted by Umesh Yadav 6 years, 4 months ago
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Yogita Ingle 6 years, 4 months ago
If nutrient solution is poorly aerated in hydroponics, the roots cannot access oxygen. In case of plants in soil, roots access oxygen through pores in soil. But in cases of plants in hydroponic treatment, oxygen has to be supplied to the roots for respiration artificially i.e. through the nutrient solution. Hence, if this solution is poorly aerated, the roots as well as the entire plant will die.
Posted by Shivam Singh Raghav 6 years, 4 months ago
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Deepak Gour 6 years, 4 months ago
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Ankit Thakur 6 years, 4 months ago
1Thank You