At a dinner of 32 guests,. 18 ate yam, 16 ate beans and 7 ate both. ·How many guests did not eat?

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Let the sets defined as follows.

A = guests who ate yam

B = guests who ate beans

According to the data given;

`n(A) = 18`

`n(B) = 16`

`n(AnnB) = 7`

From set theory;

`n(AuuB) = n(A)+n(B)-n(AnnB)`

`n(AuuB) = 18+16-7`

`n(AuuB) = 27`

`n(AuuB)` represent the amount of guests who ate something. There were 32 guests but only 27 has ate something. So the rest 5 has not eat anything from the dinner.

*The answer is 5 guests.*

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