Question

ifA={x:x is a prime number less than 12}B={x:x is factor of30}. then find. 1 AnB. 2 A-(AnB) what do you notice​

Answer 1

I had added the image. look into it for ans.

Answer 2

AnswEr:-

1) $\displaystyle\sf A \cap B = \left\{ 2,3, 5 \right\}$

2) $\displaystyle\sf A - (A \cap B) = \left\{7 , 11 \right \}$

$\rule{200}{1}$

Here,given:-

☛A ={x : x is a prime number less than 12}

We know,prime numbers less than 12:-

↠ 2 , 3, 5, 7, 11

∴ A = {2 , 3, 5, 7, 11}

$\rule{200}{1}$

Given that,

☛ B = {x : x is factors of 30}

Here,

30 = 1 × 30

30 = 2 × 15

30 = 3 × 10

30 = 5 × 6

∴ Factors of 30 = 1 ,2, 3, 5, 6, 10, 15, 30

∴ B = {1, 2, 3, 5, 6, 10, 15, 30}

Now going to your solution:-

$\sf 1) A \cap B \\\\\longrightarrow\sf \left\{2,3,5,7,11 \right \} \cap \left\{ 1, 2,3,5,6,10,15,30 \right \} \\\\\longrightarrow\sf\green{ \left\{ 2,3,5 \right \} \quad \quad - \big[Answer : 1 \big]}$

Therefore,solution for no.1:-

∴ A $\sf \cap$ B = {2 , 3, 5 }

$\rule{200}{2}$

$\sf 2) A - (A \cap B) \\\\\longrightarrow\sf \left\{2,3,5,7, 11 \right \} - (\left \{ 2,3,5,7,11 \right \} \cap \left\{ 1,2,3,5,6,10,15,30 \right \}) \\\\\longrightarrow\sf \left\{2,3,5,7,11 \right \} - \left \{2,3,5 \right \} \\\\\longrightarrow\sf\green{\left \{ 7,11 \right \} \quad \quad - \big[Answer : 2 \big]}$

Therefore,solution for no.2:-

∴ A - (A $\sf \cap$ B) = {7, 11}