Question

4.

A = (x50 < x≤ 120, x=3k, k = N}
B = (y 70 < y ≤ 150, y = 2k, k = N)
n(A\B) = ?
A) 14
B) 15
C) 16
D) 17
E) 18
please help me , give me a formula

Answer 1

Hi,

Answer 15

Explanation:

`A=\{x | 50 < x \leq 120\ and\ x=3k, k\in \mathbb{N} \}=\{ 51,54,57,...,117,120\}\\\\\#A=(120-51)/(3) +1=24\\\\B=\{y | 70 < y \leq 150\ and\ y=2k, k\in \mathbb{N} \}=\{ 70,72,74,76,...,146,148,150\} \\\\\#B=(150-70)/(2) +1=41\\\\\\A\cap B =\{z | 72 \leq z \leq 120\ and\ z=6k, k\in \mathbb{N} \}=\{ 72,78,84,...,114,120\}\\\\\#(A\cap B)=(120-72)/(6) +1=9\\\\A-B=A-(A\cap B)=\{51,54,57,60,63,66,69,75,...,105,111,117\}\\\\\#(A-(A\cap B))=24-9=\boxed{15}`