State which of the following statement are true and which ones are false . Justify your answer .
(i) `21 in {x|x ` has exactly four positive factors }
(ii) `64 in {y| ` the sun of the all the positve factors of y is 2y }
(iii) `2 in { x |x^4- 3x^3+4x^2-5x+6=0}`
(iv) 23562 `in {y|y ` is divisible by 9}

Explanation

The factors of 21 are 1,3,7 and 21. So, 21 is an element of the set .
Hence , the givn statement is true .
(ii) The factors of 64 are 1,2,4,8,16,32, and 64 .
So, 64 a is not an element of the set .
Hence , the given statement is false .
(iii) We have `x^4-3x^3+4x^2-5x+ 6 =0`
For `x= 2 ,(2)^4-3(2)^3+4(2)^2-5(2)+6 = 0`
`rArr 16-24 + 16 - 10 +6 =0`
` rArr 4= 0 ` which is not true
So 2 is not an element of the set
Hence , the given statemet is true
(iv) We have number , 23562 Sum of the digits of the number is 2+3+5+6+2= 18 which is divisible by 9
So , 23562 is an element of the set
Hence, the given statment is false.