Write the relation R = {(x, x3): x is a prime number less than 10} in roster form

(i) A = {x: x is an integer and –3 < x < 7} The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6...

(i) All the elements of this set are natural numbers as well as the divisors of 6.  Therefore, (i) matches with (c).  (ii)It can be seen that 2 and 3 are prime numbers....

A = {x: x is a natural number} = {1, 2, 3, 4, 5 …}  B ={x: x is an even natural number} = {2, 4, 6, 8 …}  C = {x:...

R = {(x, x3): x is a prime number less than 10} The prime numbers less than 10 are 2, 3, 5, and 7.  ∴ R = {(2, 8), (3, 27),...

Solution: No. Justification: Consider the positive integer 3q + 1, where q is a natural number. => (3q + 1)2 = 9q2 + 6q + 1 = 3(3q2 + 2q) + 1 = 3m + 1,...

It is (B) an irrational number 

(i) A = {x: x is an integer and –3 < x < 7} The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6...

Total non-prime numbers from 1 to 10 = 6 Required probability =6/10=3/5

(a) Let the number be (10x + y) Then, (10x + y) – (10y + x) = 18 9x – 9y = 18 x – y = 2 ...(i) and,...

(c) A = C + 3, D = B – 4, E = F – 6  C = E + 2, F = D + 3  On adding, we get A =...