Question

find the cardinal number of the set A={b:b€z and -7greater 3b-152}​

Answer 1

Answer:

A={6,10,14,….,58}

Answer 2

A4 = {b : b ∈ Z and -7 < 3b -1 ≤ 2}  

-7 < 3b - 1  

⇒ -7+1 < 3b -1+1

(Adding 1 to both sides)  

⇒ -6 < 3b  

=> (-6/3) < b

(Dividing both sides by 3)  

⇒ - 2 < b  

Again 3b - 1 ≤ 2  

⇒ 3b -1 + 1 ≤ 2+1 (Adding 1 to both sides)  

⇒ 3b ≤ 3  

⇒ b ≤ (3/3)  

(Dividing both sides by 3)  

⇒ b ≤ 1  

∴  -2 ≤ b ≤ 1  

∴ Given set A4 = {-1, 0, 1}  

∴  Cardinal number of set A4 = 3

Hope this helps