00:01
In this question we have given 4 sets and we have to find that whether the given sets are closed under addition or not.
00:07
So the first we have given p is equals to singleton 0.
00:14
Now we know that a set is closed under addition if and only if.
00:20
If we add any two terms of the given set, then the resultant summation will also belong to the given set only.
00:30
This must be true for each element of the given set.
00:34
So here we have given single turn 0.
00:37
So if we add 0 plus 0, then we will get it as 0 and 0 belongs to p.
00:42
Therefore, p is closed under addition.
00:51
Now, second we have given b as s is equals to 0, 7, 14, comma, 21, comma 28 and so on.
01:05
So here if we check then 0 plus 7 is equal to 7 this belongs to s.
01:11
Similarly 7 plus 14 is equal to 21 this also belongs to s.
01:18
Now 21 plus 14 is equals to 35.
01:25
That is also belongs to s.
01:27
Why? because this this set is infinite set having all the material.
01:32
Of 7.
01:33
So 35 is multiple of 7.
01:36
And in this set if we add any two numbers then we get a resultant number as a multiple of 7 only...