Sets Questions ...The set notation is not clear. Please immediate help is needed.?

28 not red;

30 not blue

& not either = 2 not red not blue but another

60-28-2 = 24 blue

60-30 - 2 - 28 blue,

so the venn boils down to a super set of 59 shared among two subsets of 28. The set not liking any is not part of the set or is an empty set within the set of blues and reds.

I have worked this backwards from the answer that you provide and I can now ADD the detail that is missing from your question.

your question should read:-

60 people were questioned about which of the colours red and blue they liked. SEVEN said they liked none, 28 did not like red and 30 did not like blue. By drawing a Venn diagram, find how many liked (a) blue only (b) both colours.

Someone had the shift key down when they typed a 7 and therefore typed & instead.

Now we can do the question! Please note I am unable to actually draw the Venn diagram in this format, I shall have to leave that to you.

Calling the people that like red only "R"

Calling the people that like blue only "B"

and that like both = "RB"

If 28 did not like red, it means that 60 - 28 = 32 did like red

However this 32 is made up of R + RB

R + RB = 32

Similarly if 30 people did not like blue then 60 - 30 = 30 did like blue

and therefore B + RB = 30

Add these two equations together

R + RB + B + RB = 32 + 30

R + B + 2RB = 62, ........call this Equation 1

Now we know that 60 people are interviewed and 7 like neither

Therefore 53 people like red, blue or both

In maths terms

R + B + RB = 53, ........call this Equation 2

Now you have two simultaneous equations

R + B + 2RB = 62

R + B + RB = 53

Subtract bottom from top

RB = 9

ANSWER part B) 9 people like both

BUT

we know that 30 people like B or both

therefore 30 - 9 = 21 like just blue

ANSWER part A) 21 people like blue only

(FYI the number of people that like red only is 32 - 9 = 23)

I hope that you can now draw the Venn diagram to show this