Question

40 people were asked whether they can sew and whether they can knit. 14 of them can sew and 12 of them can knit. 5 of the people who can sew can also knit. How many of the people asked can neither sew nor knit?​

Answer 1

Out of the 40 people asked, 19 people can neither sew nor knit, found by subtracting the number who can sew or knit from the total number of people.

Step-by-step explanation:

To find out how many of the 40 people asked can neither sew nor knit, we can use set theory and Venn diagrams. First, let's note the total number of people who can sew, knit, or both, which is given by the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B), where n(A ∪ B) represents the total number of people who can sew or knit, n(A) is the number who can sew, n(B) is the number who can knit, and n(A ∩ B) is the number who can do both.

Using the numbers provided:

• n(A) = 14 (can sew)
• n(B) = 12 (can knit)
• n(A ∩ B) = 5 (can sew and knit)

Thus, we calculate:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 14 + 12 - 5 = 21

This means that 21 people can sew or knit. Since there were 40 people total, the number who can neither sew nor knit is:

40 - n(A ∪ B) = 40 - 21 = 19

Therefore, 19 people cannot sew or knit.