Question

11. If X={ x:x is a prime number which is less than 15) Y={y:y is a multiple of 7,75y530),
then find i) n( X), ii) n( Y) and iii) n (X-Y)​

Answer 1

SOLUTION

GIVEN

X = { x : x is a prime number which is less than 15 }

Y= { y : y is a multiple of 7 , 7 ≤ y ≤ 30 },

TO DETERMINE

i) n( X), ii) n( Y) and iii) n (X-Y)

CONCEPT TO BE IMPLEMENTED

SET

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

The number of elements in a set S is denoted by n(S)

DIFFERENCE OF SETS

If X and Y are two sets then their difference is denoted by X - Y and defined as

X - Y = { x : x ∈ X , x ∉ Y }

EVALUATION

Here it is given that

X = { x : x is a prime number which is less than 15 }

∴ X = { 2 , 3 , 5 , 7 , 11 , 13 }

∴ n(X)

= Number of elements in the set X

= 6

Y= { y : y is a multiple of 7 , 7 ≤ y ≤ 30 }

∴ Y = { 7 , 14 , 21 , 28 }

∴ n(Y)

= Number of elements in the set Y

= 4

Again

X - Y = { x : x ∈ X , x ∉ Y }

∴ X - Y = { 2 , 3 , 5 , 11 , 13 }

∴ n(X - Y)

= Number of elements in the set X - Y

= 5

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