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Relations And Functions

Question

(i) A = $space space space equals space left curly bracket space straight x space colon space straight x space element of space straight Z right parenthesis$ and x is a root of quadratic equation x²-3x -10 = 0}

Now, x²-3x -10 = 0

$rightwards double arrow$ (x-5) (x+2) = 0

$rightwards double arrow$ x=5, -2 which are both integers.

Hence, A = {-2, 5}

(ii) B= {x :x $space element of space straight N$ , -5 < x-2 < 5}

Now, -5 < x-2 < 5

$rightwards double arrow$ -3 < x < 7

$rightwards double arrow$ x is a natural number between -3 and 7 (exclusive).

Hence, B = {1, 2, 3, 4, 5, 6}

(iii) C = {x : x is an odd prime number less than 30}

$rightwards double arrow$ x = 3, 5, 7, 11, 13, 17, 19, 23, 29

Hence C = { 3, 5, 7, 11, 13, 17, 19, 23, 29}

Solution