Question

Given € = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, set P = {1, 2, 4, 6, 8, 10} and set Q = {2, 3, 4, 5, 6, 7, 9, 12). Draw Venn Diagrams for each of the following and list the elements of the sets:
i. (P ٮ Q)'
ii. [(P ٮ Q) ∩ (P ∩ Q)] ٮ (P ٮ Q)'

Answer 1

Answer:

Given € = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, set P = {1, 2, 4, 6, 8, 10} and set Q = {2, 3, 4, 5, 6, 7, 9, 12). Draw Venn Diagrams for each of the following and list the elements of the sets:

i. (P ٮ Q)'

ii. [(P ٮ Q) ∩ (P ∩ Q)] ٮ (P ٮ Q)'

Step-by-step explanation:

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Answer 2

Give :  U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},

set P = {1, 2, 4, 6, 8, 10} and set Q = {2, 3, 4, 5, 6, 7, 9, 12).

To Find : Draw Venn Diagrams for each of the following and list the elements of the sets:

( P U Q ) '

Solution:

P = {1, 2, 4, 6, 8, 10}  

Q = {2, 3, 4, 5, 6, 7, 9, 12).

P ∩ Q  = {  2 , 4 , 6 }

P U Q  =  { 1 , 2, 3, 4, 5, 6, 7, 8 , 9, 10 , 12).

( P U Q ) '  =  { 11 , 13 , 14 , 15 }

(P U Q)  ∩ (P ∩ Q ) =  P ∩ Q

(P U Q)  ∩ (P ∩ Q )  U ( P U Q ) '   =  ( P ∩ Q )  U ( P U Q ) '

(P U Q)  ∩ (P ∩ Q )  U ( P U Q ) '   = { } = Ф

Please find attached venn diagram

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