Question

Let S = \{1, 2, 3, 4, 5, 6, 7\}, E = \{1, 3, 5, 7\}, F = \{7, 4, 6\}, G = \{1, 4\}. Use Venn diagram alone, write the values shade the regions corresponding to the following (a) EF; (c) EG$^c$; (e) E$^c \cup$(F$\cup$G); (b) E$\cup$FG; (d) EF$^c \cup$G; (f) E$\cup$G$\cup$FG.

          Let S = \{1, 2, 3, 4, 5, 6, 7\}, E = \{1, 3, 5, 7\}, F = \{7, 4, 6\}, G = \{1, 4\}. Use Venn diagram alone, write the values shade the regions corresponding to the following (a) EF; (c) EG$^c$; (e) E$^c \cup$(F$\cup$G); (b) E$\cup$FG; (d) EF$^c \cup$G; (f) E$\cup$G$\cup$FG.

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$Let S = {1, 2, 3, 4, 5, 6, 7}, E = {1, 3, 5, 7}, F = {7, 4, 6}, G = {1, 4}. Use Venn diagram alone, write the values shade the regions corresponding to the following (a) EF; (c) EG^c; (e) E^c ∪(F∪G); (b) E∪FG; (d) EF^c ∪G; (f) E∪G∪FG.$

Added by Ronald R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

11/14/2023

Step 1

Step 1: Draw a Venn diagram with three overlapping circles representing sets E, F, and G. Show more…

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Let S = {1, 2, 3, 4, 5, 6, 7}, E = {1, 3, 5, 7}, F = {7, 4, 6}, G = {1, 4}. Use Venn diagram alone, write the values shade the regions corresponding to the following (a) EF; (c) EG; (e) E (FUG); (b) EUFG; (d) EFCUG; (f) EGUFG.

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Transcript

00:01 Hi, today we are solving the question in which we are given with sets.

00:04 So here given that let u is equals to 1, 2, 3, 4, 5, 6, 7, 8.

00:14 So here u is the universal set.

00:16 We can see that an a is given as the set of 3, 6 and 8.

00:23 Then b is given as a set of 4 and 6.

00:29 And c is given as a set of 1, 6, 7 and 8.

00:36 So here we need to construct a venn diagram and place the elements in the proper region.

00:47 So first we draw a rectangle to represent the universal set u which contains all the elements from 1 to 8.

00:56 Now then we draw 3 circles inside the rectangle to represent a, b, c set.

01:02 So we place the element of each set in their respective circle making sure to account for any overlaps between the sets.

01:11 So the distribution of elements in the venn diagram will be element unique in a set.

01:23 So the element we can see unique is 3 in the given set a.

01:30 So 3 is the unique element.

01:33 Then if we see element unique in set b.

01:43 So if we see that 4 is the element that is unique in set b.

01:49 Then element unique to set c.

01:53 Element unique in set c.

01:59 If we see 1 and 7 are the unique elements that are not present in a and b.

02:06 So we can say 1 and 7 are unique element in c...

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