Relations and Functions

Relations and Functions

Question

 Match the equivalent sets amongst sets (i), (ii), (iii), (iv) with sets (a), (b), (c), (d).

 (i) space space space space space left curly bracket space straight x colon space straight x element of space bold N bold comma bold space bold 4 bold space bold less or equal than bold 6 bold space bold x bold space bold less or equal than bold space bold 6 bold right curly bracket

(ii)     { x : x is a vowel of English alphabet}

(iii)     {x : xspace space element of N, x is a divisor of 6}

(iv)     { x : xspace space space element of N, (x+1) (x-2) = 0}

(a)       {q}   (b) {1, 2, 3}     (c)   {x :x is a prime number and x space space space space space space space straight x space less or equal than space 12}

(d) space space space space space space space left curly bracket space straight x space colon space straight x space element of space bold N bold space and space straight x space less or equal than space 4 right curly bracket

Answer

Writing the sets in the tabular form, we have :
(i)  {4, 5, 6}        (ii) {a, i, o, u}    (iii) {1, 2, 3, 6}       (iv)   {23}

(a) = {q}
(b) = {1, 2, 3}
(c) = {2, 3, 5, 7, 11}
(d) = {1, 2, 3, 4}
from above, we have number of elements in (i) is the same as those in (b), similarly, others cna be matched
Hence, (i) ~ b             (ii) ~ (c)             (iii) ~ (d)        (iv) ~ (a)

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