Q9 of 58 Page 12

If Y = {1, 2, 3,..., 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

(i) a ∈ Y but a2∉ Y


(ii) a + 1 = 6, a ∈ Y


(iii) a is less than 6 and a ∈ Y

(i) Given: Y = {1, 2, 3,..., 10} where a represents any element of Y


To find: sets containing all numbers represented by a ∈ Y but a2∉ Y


Y = {1, 2, 3,..., 10}


12 = 1, 22 = 4, 32 = 9


1, 4, 9 ∈ Y ⇒ 1, 2, 3 does not satisfy given condition


Therefore,


{a: a ∈ Y and a2∉ Y}


= {4, 5, 6, 7, 8, 9, 10}


(ii) Given: Y = {1, 2, 3,..., 10} where a represents any element of Y


To find: sets containing all numbers represented by a + 1 = 6, a ∈ Y


Y = {1, 2, 3,..., 10}


a + 1 = 6 ⇒ a = 5


⇒ 5 satisfies given condition


Therefore,


{a: a + 1 = 6, a ∈ Y }


= {5}


(iii) Given: Y = {1, 2, 3,..., 10} where a represents any element of Y


To find: sets containing all numbers represented by a is less than 6 and a ∈ Y


Y = {1, 2, 3,..., 10}


a is less than 6


⇒ 1, 2, 3, 4, 5 satisfy given condition


Therefore,


{a: a is less than 6, a ∈ Y }


= {1, 2, 3, 4, 5}


More from this chapter

All 58 →
7

Given that N = {1, 2, 3 ,..., 100}. Then write

(i) the subset of N whose elements are even numbers.


(ii) the subset of N whose element are perfect square numbers.

 8

If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by

(i) 4n


(ii) n + 6


(iii)


(iv) n – 1

 10

A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20}, B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.

 11

Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.