Question

If n(A)=15 and n(B)=17 then find n(A u B u C) from the following Venn diagram.(The number in each region represents the number of elements of that region)

solve 32 and 33 and step by step.
and Don't type anything Like IdK or IDC ​

Answer 1

Answer:

37

Step-by-step explanation:

Given : n(A)=15 & n(B)=17

Now , if you look at the Circle C  , you can see the numbers 9, 4, 1, & 5.

When you combine these numbers , it will give you the value of C.

Hence,

n(C) = 9+5+1+4

Now , If you look closely , you can see that

The intersection of the circles A and B is (3 + 1),

The intersection of the circles A and C is ( 4 +1), &

The intersection of the circles B and C is (1+5)

hence ,

n(A ∩ B) = (3+1)

n(A ∩ C) = (4+1)

n(B ∩ C) = (1+5)

Also , the circle A,B and C are intersected at the middle, at value '1'

Hence ,

n(A ∩ B ∩ C). = 1

Now, let's input all the values into the formula of  A ∪ B ∪ C

The formula of A ∪ B ∪ C is given as follows :-

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(A ∩ C) − n(B ∩ C) + n(A ∩ B ∩ C).

After inputting the values in the formula, we get.

= 15 + 17 + (9+5+1+4) - (3+1) - (4+1) - (1+5) + (1) = 32 + 19 - 4 - 5 - 6 + 1

= 32 + 19 - 15 + 1

=51 - 15 + 1

=36+1

= 37

hence, 37 is the answer