In a survey of 30 consumers of detergents 5 people said they...

In a survey of 30 consumers of detergents, 5 people said they are loyal to brand A, while another 5 are loyal to brand B. Five surveyed said they do not use either brands A, B, nor C, but use some other detergents not included in the survey. A total of ten consumers said they prefer brand A, and a total of 11 said they prefer brand C. Four said they are using both A and B. There were no one who used both brands B and C. Further, almost peculiarly, no one said they used A, B, and C simultaneously. a. How many person uses brand A or brand B but not brand C? b. How many person uses both brand A and brand C?

Transcript

00:01 In the asked question, we have a survey of 30 customers of detergents.

00:05 30 customers.

00:08 Five people said they are loyal to brand a.

00:12 Five are loyal to brand a.

00:20 Another five are loyal to brand b.

00:23 Are loyal to brand b.

00:26 Five surveyed said that they don't use either brand is a, b, nor c.

00:34 We have another five, no a, b.

00:41 Or c because they use some other detergents not included in the survey we can say that they use other we have 10 customers that said they prefer brand a 10 prefer brand a and the total of 11 said they prefer c 11 prefer c 4 said they are using both a and b for use a and b they were no one who used both brands b and c then we have zero b and c furthermore no one said they used a b and c zero a b and c it's required to answer two parts in this question how many person used or uses brand a or brand b but not brand c how many persons use both brand a and brand a and brand to answer this it's preferred to make a vendagram let's make a very big one this is the total space of the 30 surveyed consumers this is for a this is for b this is for c have a here b here and c and the white space the other is for other other brands it said that five are loyal to a loyal means that they don't use any other brand than a then we have five in this area just a and another five are loyal to brand b then our loyal to brand b is this in this category we have five then we have used the first and the second information third information 5 use other then we have 5 here outside a b and c a or b or c in the white space in the remaining vendagram let's move to 10 prefer a 10 prefer a means that it might be in this area but we don't know at which section then we will leave this information now the other one says that 11 peripheral see we will leave it because it might be any of the three sections here or the four and it's the sum of these four sections and then here means the sum of these four sections we not know which section then we will leave leave it alone now we have another information that says four use a and b a and b a and b is one of these two sections again we don't know which we will leave it alone but we have very useful information zero uses a b and c a b and c is this section now we filled this with zero because we have here zero and another zero for b and c b and c is this section we have here actually b and c is this section but we have filled one with zero the other would be of course zero then we have used these two information let's get back to four use a and b one here is filled with zero the other will be four to make the total here to be four let's get back to ten to ten prefer a let's use it ten prefer a, we have said that we have this section plus this section, plus this section, plus this section, plus this section to be 10...

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