Question

If D ={ x: 2x - 1< 10, x€ N} then n(D) is​

Answer 1

n(D) is the number of elements in the set D. To find n(D), we need to determine all the natural numbers (x € N) that satisfy the inequality 2x - 1 < 10.

Starting from x = 1, we see that 2x - 1 = 2 * 1 - 1 = 1, which is less than 10. So, x = 1 is an element of D.

We can keep increasing x and checking whether 2x - 1 is less than 10. When x = 6, 2x - 1 = 2 * 6 - 1 = 11, which is not less than 10. So, the largest x that satisfies the inequality is 5.

Therefore, the set D consists of the natural numbers 1, 2, 3, 4, and 5. Hence, n(D) = 5.