Let R 1 and R 2 be relations on the set 1 , 2 , … , 50 such that R 1 = p , p n : p is a prime and n ≥ 0 is an integer and R 2 = p , p n : p is a prime and n = 0 or 1 . Then, the number of elements in R 1 - R 2 is ____.

Question

Let R 1 and R 2 be relations on the set 1 , 2 , &#8230; , 50 such that R 1 = p , p n : p is a prime and n &#8805; 0 is an integer and R 2 = p , p n : p is a prime and n = 0 or 1 . Then, the number of elements in R 1 - R 2 is ____.

Quantrex Academy · Accepted Answer

Correct answer: 0

Here, p , p n &#8712; 1 , 2 , &#8230; 50 Now p can take values 2 , 3 , 5 , 7 , 11 , 13 , 17 , 23 , 29 , 31 , 37 , 41 , 43 and 47 . &#8756; R 1 = 2 , 2 0 , 2 , 2 1 &#8230; 2 , 2 5 , 3 , 3 0 , &#8230; 3 , 3 3 , 5 , 5 0 , &#8230; 5 , 5 2 , 7 , 7 0 , &#8230; 7 , 7 2 , 11 , 11 0 , 11 , 11 1 , . . . 47 , 47 0 , 47 , 47 1 R 2 = 2 , 2 0 , 2 , 2 1 , 3 , 3 0 , 3 , 3 1 . . . . 47 , 47 0 , 47 , 47 1 Now R 1 - R 2 &#8801; R 1 &#8745; R 2 ' So R 1 - R 2 = 2 , 2 2 , 2 , 2 3 , 2 , 2 4 , 2 , 2 5 , 3 , 3 2 , 3 , 3 3 , 5 , 5 2 , 7 ,

Let R 1 and R 2 be relations on the set 1 , 2 , … , 50 such that R 1 = p , p n : p is a prime and n ≥ 0 is an integer and R 2 = p , p n : p is a prime and n = 0 or 1 . Then, the number of elements in R 1 - R 2 is ____.

Correct answer

Step-by-step solution

More from Sets and Relations

Let R 1 and R 2 be relations on the set 1 , 2 , &#8230; , 50 such that R 1 = p , p n : p is a prime and n &#8805; 0 is an integer and R 2 = p , p n : p is a prime and n = 0 or 1 . Then, the number of elements in R 1 - R 2 is ____.

Correct answer

Step-by-step solution

More from Sets and Relations

Let R 1 and R 2 be relations on the set 1 , 2 , … , 50 such that R 1 = p , p n : p is a prime and n ≥ 0 is an integer and R 2 = p , p n : p is a prime and n = 0 or 1 . Then, the number of elements in R 1 - R 2 is ____.