Question

which of the following sets are equal.give reasons
a. {2,3,4}and {5,6,7}
b. {x/x is a natural number less than 5 and {0,1,2,3}
c. set of vowels in the english alphabet and the set of first five even numbers
d. set of all vowels in the word BATA and the set of vowels in the word AT​

Answer 1

Answer:

a,b are not equal sets

c,d are equal sets

Answer 2

❖ Which sets are equal ?

★ Two sets are equal if they have exactly the same elements.

( no matter in which order elements are arranged)

Example :

Let,

A = { 1 , 2 , 3 , 4 }

B = { 2 , 3 , 1 , 4 }

Since, A and B have exactly same elements

therefore

A = B

❖ Solution :-

_____________________________

a)

set { 2 , 3 , 5 } and set { 5 , 6 , 7}

don't have same elements

Hence,

{2, 3,5} ≠ {5,6,7}

_____________________________

b)

set of natural numbers less than 5 will be

{ 1 , 2 , 3 , 4 }

and

second set is { 0 , 1 , 2 , 3 }

these two sets don't have exactly same elements

Hence,

{1, 2,3,4} ≠ { 0,1,2,3}

_____________________________

c)

set of vowels in English alphabet is

{ a, e, i, o, u }

set of first five even numbers is

{ 2 , 4 , 6 , 8 , 10 }

Since, these sets don't have exactly same elements

{a, e,i,o,u} ≠ {2, 4,6,8,10}

____________________________

d)

set of vowels in word BATA

{ A }

and

set of vowels in the word AT

{ A }

since,

two sets have exactly same elements

therefore,

{ A } = { A }

_____________________________

Know : what are equivalent sets

Two sets are equivalent if they have exactly same number of elements or same cardinality.

Example :

Let,

A = { 1 , 2 , 3 }

B = { a, b, c }

since,

n (A)= 3

n (B) = 3

therefore,

Sets A and B are equivalent.