Which of the following are examples of the null set Set of odd natural numbers divisible by 2

(i) A set of odd natural numbers divisible by 2 is a null set because no odd number is divisible by 2. (ii) A set of even prime numbers is not a...

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: set of real numbers  Q: set of rational numbers  Therefore, R – Q is a set of irrational numbers.

U = N: Set of natural numbers  (i) {x: x is an even natural number}´ = {x: x is an odd natural number}  (ii) {x: x is an odd natural number}´ =...

n2 - 1 is divisible by 8, if n is an odd integer 

Let, a = 2p+1, p∈N and b = 2q+1 , q∈N\(\cup\){0} \(\because\) a > b ⇒ 2p+1 > 2q+1 ⇒ p > q \(\frac{a+b}{2}\) = \(\frac{2p+1+2q+1}{2}\) = p+q+1 \(\frac{a-b}{2}\) = \(\frac{2p+1-(2q+1)}{2}\) = p-q Case-I: \(\frac{a+b}{2}\) is odd which implies p+q+1 is odd \(\Rightarrow\) p+q is even (\(\because\) odd - 1 = even) \(\Rightarrow\) p+q-2q...

R: set of real numbers Q: set of rational numbers Therefore, R – Q is a set of irrational numbers.

R = {(x, y): y = x + 5, x is a natural number less than 4, x, y ∈ N} The natural numbers less than 4 are 1, 2, and...

Divisible by 4 => last 2 digits divisible by 4 => ends in 12, 24, 32, 44 or 52 So, 53 x 5 = 625