Question

If the total number of seniors in the academy is 84, what is the total number of students who belong to the set (~M ∩ C) ∩ ~B?

Answer 1

7

19

26

49

Answer 2

i haven't seen the symbol ~ in set theory before. what does it mean?

Answer 3

That's what I'm trying to figure out. Everything else, I know what to do.

Answer 4

it means 'negation' in logic
- not sure if this applies here
if it does then
(~M ∩ C) means the intersection of C with all elements not in M

Answer 5

which is the set { 19 , 11, 21}

Answer 6

and finally we need the set which is intersection of this set with set of all elements not in B

Answer 7

oops error the first set (~M ∩ C) is {11, 19} 21 is incorrect

Answer 8

so ∩ ~B = { 19, 7, 14}
and this intersect (11,19) = { 19}

so i think thats your answer

Answer 9

oh you require the total number of students - that is the number of elements in the set

- thats 19

Answer 10

so if my initial premise is correct then thats the correct answer

Answer 11

in the uk we use a different symbol for the complement of a set we use '

so A' means the set of all elements not in set A

Answer 12

Oh, i get it now. Thanks for your help!

Answer 13

19