B. Sketch these Cartesian products on the x-y plane ℝ^2 (or...

B. Sketch these Cartesian products on the x-y plane $\mathbb{R}^2$ (or $\mathbb{R}^3$ for the last two). 9. \{1,2,3\} \times \{-1,0,1\} 10. \{-1,0,1\} \times \{1,2,3\} 11. [0,1] \times [0,1] 12. [-1,1] \times [1,2] 13. \{1,1.5,2\} \times [1,2] 14. [1,2] \times \{1,1.5,2\} 15. \{1\} \times [0,1] 16. [0,1] \times \{1\} 17. $\mathbb{N} \times \mathbb{Z}$ 18. $\mathbb{Z} \times \mathbb{Z}$ 19. [0,1] \times [0,1] \times [0,1] 20. \{$(x, y) \in \mathbb{R}^2 : x^2 + y^2 \le 1\} \times [0,1]$

Transcript

00:01 There are 12 subparts in this question.

00:03 So first, let me take up question 10.

00:07 Question 10.

00:08 It says minus 1, 0 and 1 cross 1, 2, 3.

00:15 So what you do, simply plot minus 1, 0 and 1 on the x axis.

00:23 On the y -axis, you must plot 1, 2 and 3.

00:28 And now all the points wherever x and y have just plot them like for example over here we have 1 comma 1 right similarly this point and this point these points will be taken into consideration also since 0 is also a point so this will also be taken into consideration.

00:52 So there are three elements in the first one and the three in the second so nine points we got nine points in this question is done.

00:59 Next i can solve for you question 11.

01:03 So question 11 it has continuous, continuous variable, okay.

01:08 So 0 and 1 and this continuous so all of them have to be plotted right? again 0 and 1 because it is in the x -axis in the y -axis 2.

01:19 So what you do first you take the region, you have to take the region.

01:27 So for x equal to 1, just draw the line.

01:31 Line x equal to 1 and then draw the line y equal to 1 and then x equal to 0 and y equal to 0 are the axis itself and just shade the region correct shade the region and since both are inclusive so you must be taking this in bold lines not in the dotted lines but bold lines this is the required graph okay nice so let me move on let me move on now we can do question 70 so question 70 it says n cross said what you do plot n that is the set of natural numbers in the x axis is 1 2 3 and like that and now in the y axis plot z that is the set of integers so this is then 1, 2, 3 and so on, like that minus 1, minus 2, minus 3, and so on...

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