Question

in a certain class, 22 pupils take one or more of chemistry, economic, government. 12 take economic (E), 8 take government (G) and 7 take chemistry (C). Nobody take economic and chemistry, and 4 pupils take economic and government. (ai) Using set notation and the letters indicated above, write down the two statement in the last information. (aii) Draw a venn diagram to illustrate the information ( bi ) both chemistry and government? ( bii ) government only? (This is sets )​

Answer 1

Answer:

ai) n(E⋂C) = ∅ = null

n(E⋂G) = 4

aii) see attachment

bi) n(C⋂G) = x = 1

bii) n(G) only = 3

Step-by-step explanation:

Let chemistry = C

Economic = E

Government = G

n(E) = 12

n(G) = 8

n(C) = 7

ai) number of pupils for economics and chemistry = 0

number of pupils for economics and government = 4

The set notation for both:

n(E⋂C) = ∅ = null

n(E⋂G) = 4

aii) find attached the Venn diagram

bi) n(C⋂G) = ?

Let number of n(C⋂G) = x

From the Venn diagram

n(C) only = 12-4 = 8

n(G) only = 8-(4+x) = 4-x

n(E) only = 7-x

n(E⋂C⋂G) = 0

n(E⋂C) = 0

n(E⋂G) = 4

Total: 8+ 4-x + 7-x + x + 0+0+4 = 22

23 -x = 22

23-22 = x

x = 1

n(C⋂G) = x = 1

Number of pupils that take both chemistry and government = 1

(bii) government only = n(G) only = 4-x

n(G) only = 4-1 = 3

Number of students that take government only = 3