Thread: Venn diagram

can someone please tell me if am doing this question right

in a set of 35 people, 23 are wearing hats, 25 are wearing gloves and 30 are wearing either hats or gloves.

how many people are wearing:

(i) both hat and gloves
(ii) neither hat or gloves

i) first i take 23 away from 30 to get 7 gloves and then i take 25 from 30 to get 5 hats next i add them together to get 12 then i take it away from 30 to get the ANSWER of 18 that wear both hats and gloves

ii) i presume the answer is 5?

Hello, red55!

In a set of 35 people, 23 are wearing hats, 25 are wearing gloves
and 30 are wearing either hats or gloves.

How many people are wearing:
. . (i) both hat and gloves
. . (ii) neither hat or gloves

i) First I take 23 away from 30 to get 7 gloves (only),
and then i take 25 from 30 to get 5 hats (only).
Next I add them together to get 12,
then I take it away from 30 to get the ANSWER of 18 . . . . Right!

I assume you constructed the Venn diagram
. . or you could have used this formula:

. . n(H U G) .= .n(H) + n(G) - n(H ∩ G)
. . . . .↓ . - . - . . .↓ . . . . ↓ . . . . . .↓
. . . . 30 . . .= . .23 .+ -25 .- .n(H ∩ G)


Therefore: .n(H ∩ G) .= .23 + 25 - 30 .= .18

ii) i presume the answer is 5? . . . . Yes!

Good work!