Sets, Relations & Functions Question - None

Question

Let R1 = {(p, pn) : p prime, n ≥0, pn ≤50} and R2 = {(p, pn) : p prime, n = 0 or 1} on {1, . . . , 50}. The number of elements in R1 −R2 is:

Accepted Answer

Step 1: Since R2 covers n = 0 and n = 1, elements of R1 -R2 have n \geq2.

7

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Step 2: For each prime p, find all n \geq2 with pn \leq50:

Prime p
Powers pn (n \geq2) in {1, . . . , 50}
Count
2
4, 8, 16, 32
(26 = 64 > 50)
4
3
9, 27
(34 = 81 > 50)
2
5
25
(53 = 125 > 50)
1
7
49
(73 = 343 > 50)
1
\geq11
112 = 121 > 50 — none
0
Total
8

Question:

Step-by-Step Solution

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