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Note that P shares two common elements with R (4, 16) and the only common elements between P and Q is also 4 and 16. Since R is a subset of Q, the Venn diagram should look like P only intersects with R. There are no elements that are in P and Q but not R. 

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Ε = { 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

P = { 4,9,16}

Q = { 4,6,8,10,12,14,16,18,20}

R = { 4,8,12,16,20

R is subset of Q

P intersect Q with common element 4 and 16.

R also intersect Q with element 4.

Think your Venn diagram is correct just individual element you had ignored 20. Pls be careful on definition of E which is <= 20.

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