INTERMEDIATE LEVEL
11. It is given that
M= {x: x is a perfect square such that
0 < x < 70)
and P = {x : x is a perfect cube such that
0 < x < 70}
(i) List all the elements in Mand Pin set notation.
(ii) Draw a Venn diagram to represent the sets M
and P.
(iii) From the Venn diagram, list all the elements in
Mn Pin set notation.
Answers
Given : M= {x : x is a perfect square such that 0 < x < 70} and
P = {x : x is a perfect cube such that 0 < x < 70}.
To Find :
(i) List all the elements in M and P in set notation.
(ii) Draw a Venn diagram to represent the sets M and P.
(iii) From the Venn diagram, list all the elements in M n P in set notation.
Solution:
M= {x : x is a perfect square such that 0 < x < 70}
1² = 1 , 2² = 4 , 3² = 9 , 4² = 16 , 5² = 25 , 6² = 36 , 7² = 49 , 8² = 64
9² = 81 > 70
Hence
M = { 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 }
P = {x : x is a perfect cube such that 0 < x < 70}.
1³ = 1 , 2³ = 8 , 3³ = 27 , 4³ = 64 ,
5³ = 125 > 70
P = { 1 , 8 , 27 , 64 }
Venn Diagram attached
M n P = M ∩ P = { 1 , 64}
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