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

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