Question

Let A = {x : 2x² + 3x - 2 = 0} and B = {x : x² + 3x - 4 = 0 } find (A U B) × (A Π B)​

Answer 1

Given :

• A = {x: 2x² + 3x - 2 = 0 }
• B = {x : x² + 3x - 4 = 0 }

To find :

• (A U B ) × (A Π B )

Solution :-

The first set is ,

• A ={x : 2x² + 3x - 2 = 0}

Solving the Quadratic equation ,

• 2x² + 3x - 2 = 0
• 2x² + 4x - x - 2 = 0
• 2x( x + 2) -1( x + 2 ) = 0
• (2x -1) ( x + 2) = 0
• x = 0.5 , -2

Hence ,

• A ={0.5, -2}

The second set is ,

• B ={ x :x² + 3x - 4 = 0 }

Solving the Quadratic equation ,

• x² + 3x - 4 = 0
• x² + 4x - x - 4 = 0
• x( x + 4)-1 ( x +4) = 0
• (x + 4) ( x -1) = 0
• x = 1 , -4

Hence ,

• B ={1,4}

Now ,

• A U B = { 0.5 , 1 , 4 , -2}
• A Π B = {∅ }

Since AΠ B is a null set , hence ,

• A × B = {∅}